A332286 -id:A332286 - cp's OEIS frontend

A332282 Numbers whose unsorted prime signature is not unimodal.

300, 588, 600, 980, 1176, 1200, 1452, 1500, 1960, 2028, 2100, 2205, 2352, 2400, 2420, 2904, 2940, 3000, 3300, 3380, 3388, 3468, 3900, 3920, 4056, 4116, 4200, 4332, 4410, 4704, 4732, 4800, 4840, 5100, 5445, 5700, 5780, 5808, 5880, 6000, 6348, 6468, 6600, 6615

Offset: 1

Gus Wiseman, Feb 19 2020

nonn

The unsorted prime signature of a positive integer (row n of A124010) is the sequence of exponents it is prime factorization.
A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
Also Heinz numbers of integer partitions with non-unimodal run-lengths. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

			The sequence of terms together with their prime indices begins:
   300: {1,1,2,3,3}
   588: {1,1,2,4,4}
   600: {1,1,1,2,3,3}
   980: {1,1,3,4,4}
  1176: {1,1,1,2,4,4}
  1200: {1,1,1,1,2,3,3}
  1452: {1,1,2,5,5}
  1500: {1,1,2,3,3,3}
  1960: {1,1,1,3,4,4}
  2028: {1,1,2,6,6}
  2100: {1,1,2,3,3,4}
  2205: {2,2,3,4,4}
  2352: {1,1,1,1,2,4,4}
  2400: {1,1,1,1,1,2,3,3}
  2420: {1,1,3,5,5}
  2904: {1,1,1,2,5,5}
  2940: {1,1,2,3,4,4}
  3000: {1,1,1,2,3,3,3}
  3300: {1,1,2,3,3,5}
  3380: {1,1,3,6,6}

MathWorld, Unimodal Sequence

The opposite version is A332642.
These are the Heinz numbers of the partitions counted by A332281.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
Cf. A001523, A007052, A056239, A112798, A124010, A227038, A332280, A332284, A332286, A332639, A332643, A332671.

unimodQ[q_]:=Or[Length[q]==1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Select[Range[1000],!unimodQ[Last/@FactorInteger[#]]&]

A332281 Number of integer partitions of n whose run-lengths are not unimodal.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 6, 10, 16, 24, 33, 51, 70, 100, 137, 189, 250, 344, 450, 597, 778, 1019, 1302, 1690, 2142, 2734, 3448, 4360, 5432, 6823, 8453, 10495, 12941, 15968, 19529, 23964, 29166, 35525, 43054, 52173, 62861, 75842, 91013, 109208

Offset: 0

Gus Wiseman, Feb 19 2020

nonn

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing followed by a weakly decreasing sequence.

			The a(10) = 1 through a(15) = 10 partitions:
  (33211)  (332111)  (44211)    (44311)     (55211)      (44322)
                     (3321111)  (333211)    (433211)     (55311)
                                (442111)    (443111)     (443211)
                                (33211111)  (3332111)    (533211)
                                            (4421111)    (552111)
                                            (332111111)  (4332111)
                                                         (4431111)
                                                         (33321111)
                                                         (44211111)
                                                         (3321111111)

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Unimodal Sequence

The complement is counted by A332280.
The Heinz numbers of these partitions are A332282.
The opposite version is A332639.
Unimodal compositions are A001523.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
Cf. A007052, A025065, A072706, A100883, A332283, A332284, A332286, A332287, A332579, A332638, A332640, A332641, A332642.

b:= proc(n, i, m, t) option remember; `if`(n=0, 1,
     `if`(i<1, 0, add(b(n-i*j, i-1, j, t and j>=m),
      j=1..min(`if`(t, [][], m), n/i))+b(n, i-1, m, t)))
    end:
a:= n-> combinat[numbpart](n)-b(n$2, 0, true):
seq(a(n), n=0..65);  # Alois P. Heinz, Feb 20 2020

unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]]
Table[Length[Select[IntegerPartitions[n],!unimodQ[Length/@Split[#]]&]],{n,0,30}]
(* Second program: *)
b[n_, i_, m_, t_] := b[n, i, m, t] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1, j, t && j >= m], {j, 1, Min[If[t, Infinity, m], n/i]}] + b[n, i - 1, m, t]]];
a[n_] := PartitionsP[n] - b[n, n, 0, True];
a /@ Range[0, 65] (* Jean-François Alcover, May 10 2021, after Alois P. Heinz *)

A335373 Numbers k such that the k-th composition in standard order (A066099) is not unimodal.

Original entry on oeis.org

22, 38, 44, 45, 46, 54, 70, 76, 77, 78, 86, 88, 89, 90, 91, 92, 93, 94, 102, 108, 109, 110, 118, 134, 140, 141, 142, 148, 150, 152, 153, 154, 155, 156, 157, 158, 166, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 198

Offset: 1

Gus Wiseman, Jun 03 2020

nonn

A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

			The sequence together with the corresponding compositions begins:
  22: (2,1,2)
  38: (3,1,2)
  44: (2,1,3)
  45: (2,1,2,1)
  46: (2,1,1,2)
  54: (1,2,1,2)
  70: (4,1,2)
  76: (3,1,3)
  77: (3,1,2,1)
  78: (3,1,1,2)
  86: (2,2,1,2)
  88: (2,1,4)
  89: (2,1,3,1)
  90: (2,1,2,2)
  91: (2,1,2,1,1)
  92: (2,1,1,3)
  93: (2,1,1,2,1)
  94: (2,1,1,1,2)

The dual version (non-co-unimodal compositions) is A335374.
The case that is not co-unimodal either is A335375.
Unimodal compositions are A001523.
Unimodal normal sequences are A007052.
Unimodal permutations are A011782.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
Numbers with non-unimodal unsorted prime signature are A332282.
Partitions with non-unimodal 0-appended first differences are A332284.
Non-unimodal permutations of the multiset of prime indices of n are A332671.
Cf. A000120, A029931, A048793, A066099, A070939, A334299.
Cf. A072704, A332281, A332286, A332287, A332639, A332642, A332669, A332672.

unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Select[Range[0,200],!unimodQ[stc[#]]&]

A332284 Number of integer partitions of n whose first differences (assuming the last part is zero) are not unimodal.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 2, 4, 6, 12, 18, 28, 42, 62, 86, 123, 168, 226, 306, 411, 534, 704, 908, 1165, 1492, 1898, 2384, 3011, 3758, 4673, 5799, 7168, 8792, 10804, 13192, 16053, 19505, 23633, 28497, 34367, 41283, 49470, 59188, 70675, 84113, 100048, 118689, 140533

Offset: 0

Gus Wiseman, Feb 20 2020

nonn

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

			The a(6) = 1 through a(11) = 18 partitions:
  (2211)  (331)    (431)     (441)      (541)       (551)
          (22111)  (3311)    (4311)     (3322)      (641)
                   (22211)   (32211)    (3331)      (4331)
                   (221111)  (33111)    (4411)      (4421)
                             (222111)   (33211)     (5411)
                             (2211111)  (42211)     (33221)
                                        (43111)     (33311)
                                        (222211)    (44111)
                                        (322111)    (52211)
                                        (331111)    (322211)
                                        (2221111)   (332111)
                                        (22111111)  (422111)
                                                    (431111)
                                                    (2222111)
                                                    (3221111)
                                                    (3311111)
                                                    (22211111)
                                                    (221111111)

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400
Eric Weisstein's World of Mathematics, Unimodal Sequence.

The complement is counted by A332283.
The strict version is A332286.
The Heinz numbers of these partitions are A332287.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences appear to be A328509.
Partitions with non-unimodal run-lengths are A332281.
Heinz numbers of partitions with non-unimodal run-lengths are A332282.
Cf. A001523, A007052, A332280, A332285, A332288, A332579, A332638, A332639, A332640, A332642.

unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Table[Length[Select[IntegerPartitions[n],!unimodQ[Differences[Append[#,0]]]&]],{n,30}]

A332287 Heinz numbers of integer partitions whose first differences (assuming the last part is zero) are not unimodal.

Original entry on oeis.org

36, 50, 70, 72, 98, 100, 108, 140, 144, 154, 180, 182, 196, 200, 216, 225, 242, 250, 252, 280, 286, 288, 294, 300, 308, 324, 338, 350, 360, 363, 364, 374, 392, 396, 400, 418, 429, 432, 441, 442, 450, 462, 468, 484, 490, 494, 500, 504, 507, 540, 550, 560, 561

Offset: 1

Gus Wiseman, Feb 21 2020

nonn

A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), which gives a bijective correspondence between positive integers and integer partitions.

			The sequence of terms together with their prime indices begins:
   36: {1,1,2,2}
   50: {1,3,3}
   70: {1,3,4}
   72: {1,1,1,2,2}
   98: {1,4,4}
  100: {1,1,3,3}
  108: {1,1,2,2,2}
  140: {1,1,3,4}
  144: {1,1,1,1,2,2}
  154: {1,4,5}
  180: {1,1,2,2,3}
  182: {1,4,6}
  196: {1,1,4,4}
  200: {1,1,1,3,3}
  216: {1,1,1,2,2,2}
  225: {2,2,3,3}
  242: {1,5,5}
  250: {1,3,3,3}
  252: {1,1,2,2,4}
  280: {1,1,1,3,4}
For example, the prime indices of 70 with 0 appended are (4,3,1,0), with differences (-1,-2,-1), which is not unimodal, so 70 belongs to the sequence.

MathWorld, Unimodal Sequence

The enumeration of these partitions by sum is A332284.
Not assuming the last part is zero gives A332725.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
Partitions with non-unimodal run-lengths are A332281.
Cf. A001523, A007052, A332280, A332282, A332283, A332285, A332286, A332288, A332294, A332579, A332639, A332642.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Select[Range[1000],!unimodQ[Differences[Append[Reverse[primeMS[#]],0]]]&]

A332285 Number of strict integer partitions of n whose first differences (assuming the last part is zero) are unimodal.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 5, 8, 9, 11, 13, 15, 17, 22, 25, 29, 34, 39, 42, 53, 58, 64, 75, 84, 93, 111, 122, 134, 152, 169, 184, 212, 232, 252, 287, 315, 342, 389, 419, 458, 512, 556, 602, 672, 727, 787, 870, 940, 1012, 1124, 1209, 1303, 1431, 1540, 1655, 1821

Offset: 0

Gus Wiseman, Feb 21 2020

nonn

First differs from A000009 at a(8) = 5, A000009(8) = 6.

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

			The a(1) = 1 through a(9) = 8 partitions:
  (1)  (2)  (3)   (4)   (5)   (6)    (7)    (8)    (9)
            (21)  (31)  (32)  (42)   (43)   (53)   (54)
                        (41)  (51)   (52)   (62)   (63)
                              (321)  (61)   (71)   (72)
                                     (421)  (521)  (81)
                                                   (432)
                                                   (531)
                                                   (621)
For example, (4,3,1,0) has first differences (-1,-2,-1), which is not unimodal, so (4,3,1) is not counted under a(8).

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500
Eric Weisstein's World of Mathematics, Unimodal Sequence.

The non-strict version is A332283.
The complement is counted by A332286.
Unimodal compositions are A001523.
Unimodal normal sequences appear to be A007052.
Unimodal permutations are A011782.
Partitions with unimodal run-lengths are A332280.
Cf. A025065, A072706, A115981, A227038, A332282, A332284, A332287, A332288, A332577, A332638, A332642.

unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,unimodQ[Differences[Append[#,0]]]]&]],{n,0,30}]

A332579 Number of integer partitions of n covering an initial interval of positive integers with non-unimodal run-lengths.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 4, 7, 8, 10, 14, 19, 22, 30, 36, 43, 56, 69, 80, 101, 121, 141, 172, 202, 234, 282, 332, 384, 452, 527, 602, 706, 815, 929, 1077, 1236, 1403, 1615, 1842, 2082, 2379, 2702, 3044, 3458, 3908, 4388, 4963, 5589, 6252

Offset: 0

Gus Wiseman, Feb 25 2020

nonn

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

Also the number of strict integer partitions of n whose negated first differences (assuming the last part is zero) are not unimodal.

			The a(10) = 1 through a(16) = 7 partitions:
  33211  332111  3321111  333211    433211     443211      443221
                          33211111  3332111    4332111     3333211
                                    332111111  33321111    4432111
                                               3321111111  33322111
                                                           43321111
                                                           333211111
                                                           33211111111

MathWorld, Unimodal Sequence

The complement is counted by A332577.
Not requiring the partition to cover an initial interval gives A332281.
The opposite version is A332286.
A version for compositions is A332743.
Partitions covering an initial interval of positive integers are A000009.
Unimodal compositions are A001523.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
Numbers whose prime signature is not unimodal are A332282.
Partitions whose 0-appended first differences are unimodal are A332283.
Compositions whose negated run-lengths are not unimodal are A332727.
Cf. A007052, A100883, A107429, A227038, A332280, A332284, A332638, A332639, A332640, A332671, A332672, A332728.

normQ[m_]:=m=={}||Union[m]==Range[Max[m]];
unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Table[Length[Select[IntegerPartitions[n],normQ[#]&&!unimodQ[Length/@Split[#]]&]],{n,0,30}]

A332728 Number of integer partitions of n whose negated first differences (assuming the last part is zero) are unimodal.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 7, 8, 10, 13, 14, 17, 22, 24, 28, 34, 37, 43, 53, 56, 64, 76, 83, 93, 111, 117, 131, 153, 163, 182, 210, 225, 250, 284, 304, 332, 377, 401, 441, 497, 529, 576, 647, 687, 745, 830, 883, 955, 1062, 1127, 1216, 1339, 1422, 1532, 1684, 1779, 1914

Offset: 0

Gus Wiseman, Feb 26 2020

nonn

First differs from A000041 at a(6) = 10, A000041(6) = 11.

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

			The a(1) = 1 through a(8) = 10 partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (21)   (22)    (32)     (33)      (43)       (44)
             (111)  (31)    (41)     (42)      (52)       (53)
                    (1111)  (221)    (51)      (61)       (62)
                            (11111)  (222)     (331)      (71)
                                     (321)     (421)      (332)
                                     (111111)  (2221)     (431)
                                               (1111111)  (521)
                                                          (2222)
                                                          (11111111)

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600
Eric Weisstein's World of Mathematics, Unimodal Sequence.
Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

The non-negated version is A332283.
The non-negated complement is counted by A332284.
The strict case is A332577.
The case of run-lengths (instead of differences) is A332638.
The complement is counted by A332744.
The Heinz numbers of partitions not in this class are A332287.
Unimodal compositions are A001523.
Compositions whose negation is unimodal are A332578.
Compositions whose run-lengths are unimodal are A332726.
Cf. A007052, A332280, A332285, A332286, A332639, A332642, A332669, A332670, A332741.

unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Table[Length[Select[IntegerPartitions[n],unimodQ[-Differences[Append[#,0]]]&]],{n,0,30}]

A332744 Number of integer partitions of n whose negated first differences (assuming the last part is zero) are not unimodal.

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 4, 7, 12, 17, 28, 39, 55, 77, 107, 142, 194, 254, 332, 434, 563, 716, 919, 1162, 1464, 1841, 2305, 2857, 3555, 4383, 5394, 6617, 8099, 9859, 12006, 14551, 17600, 21236, 25574, 30688, 36809, 44007, 52527, 62574, 74430, 88304, 104675, 123799

Offset: 0

Gus Wiseman, Feb 27 2020

nonn

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

			The a(4) = 1 through a(9) = 17 partitions:
  (211)  (311)   (411)    (322)     (422)      (522)
         (2111)  (2211)   (511)     (611)      (711)
                 (3111)   (3211)    (3221)     (3222)
                 (21111)  (4111)    (3311)     (4221)
                          (22111)   (4211)     (4311)
                          (31111)   (5111)     (5211)
                          (211111)  (22211)    (6111)
                                    (32111)    (32211)
                                    (41111)    (33111)
                                    (221111)   (42111)
                                    (311111)   (51111)
                                    (2111111)  (222111)
                                               (321111)
                                               (411111)
                                               (2211111)
                                               (3111111)
                                               (21111111)
For example, the partition y = (4,2,1,1,1) has negated 0-appended first differences (2,1,0,0,1), which is not unimodal, so y is counted under a(9).

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600
Eric Weisstein's World of Mathematics, Unimodal Sequence.
Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

The complement is counted by A332728.
The non-negated version is A332284.
The strict case is A332579.
The case of run-lengths (instead of differences) is A332639.
The Heinz numbers of these partitions are A332832.
Unimodal compositions are A001523.
Non-unimodal compositions are A115981.
Heinz numbers of partitions with non-unimodal run-lengths are A332282.
Partitions whose 0-appended first differences are unimodal are A332283.
Compositions whose negation is unimodal are A332578.
Numbers whose negated prime signature is not unimodal are A332642.
Compositions whose negation is not unimodal are A332669.
Cf. A059204, A227038, A332280, A332285, A332286, A332287, A332638, A332670, A332725, A332726.

unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Table[Length[Select[IntegerPartitions[n],!unimodQ[-Differences[Append[#,0]]]&]],{n,0,30}]

A072707 Number of non-unimodal compositions of n into distinct terms.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 2, 2, 4, 6, 24, 26, 46, 64, 100, 224, 276, 416, 590, 850, 1144, 2214, 2644, 3938, 5282, 7504, 9776, 13704, 21984, 27632, 38426, 51562, 69844, 91950, 123504, 159658, 246830, 303400, 416068, 540480, 730268, 933176, 1248110

Offset: 0

Henry Bottomley, Jul 04 2002

Also the number of compositions of n into distinct terms whose negation is not unimodal. - Gus Wiseman, Mar 05 2020

			a(6)=2 since 6 can be written as 2+1+3 or 3+1+2.
From _Gus Wiseman_, Mar 05 2020: (Start)
The a(6) = 2 through a(9) = 6 strict compositions:
  (2,1,3)  (2,1,4)  (2,1,5)  (2,1,6)
  (3,1,2)  (4,1,2)  (3,1,4)  (3,1,5)
                    (4,1,3)  (3,2,4)
                    (5,1,2)  (4,2,3)
                             (5,1,3)
                             (6,1,2)
(End)

Eric Weisstein's World of Mathematics, Unimodal Sequence

The complement is counted by A072706.
The non-strict version is A115981.
The case where the negation is not unimodal either is A332874.
Unimodal compositions are A001523.
Strict compositions are A032020.
Non-unimodal permutations are A059204.
A triangle for strict unimodal compositions is A072705.
Non-unimodal sequences covering an initial interval are A328509.
Numbers whose prime signature is not unimodal are A332282.
Strict partitions whose 0-appended differences are not unimodal are A332286.
Compositions whose negation is unimodal are A332578.
Compositions whose negation is not unimodal are A332669.
Non-unimodal compositions covering an initial interval are A332743.
Cf. A007052, A072704, A107429, A227038, A329398, A332281, A332284, A332285, A332579, A332870.

unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&!unimodQ[#]&]],{n,0,16}] (* Gus Wiseman, Mar 05 2020 *)

a(n) = A032020(n) - A072706(n) = Sum_{k} A059204(k) * A060016(n, k).

cp's OEIS Frontend

A332282 Numbers whose unsorted prime signature is not unimodal.

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A332281 Number of integer partitions of n whose run-lengths are not unimodal.

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A335373 Numbers k such that the k-th composition in standard order (A066099) is not unimodal.

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A332284 Number of integer partitions of n whose first differences (assuming the last part is zero) are not unimodal.

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A332287 Heinz numbers of integer partitions whose first differences (assuming the last part is zero) are not unimodal.

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A332285 Number of strict integer partitions of n whose first differences (assuming the last part is zero) are unimodal.

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A332579 Number of integer partitions of n covering an initial interval of positive integers with non-unimodal run-lengths.

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A332728 Number of integer partitions of n whose negated first differences (assuming the last part is zero) are unimodal.

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