A322878
Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals five.
Original entry on oeis.org
0, 1, 19, 171, 1293, 9320, 66992, 488526, 3637440, 27735903, 216992278, 1743777862, 14401360577, 122242150172, 1066284279026, 9554869690126, 87923414758506, 830459368379431, 8047463255217118, 79967170844047637, 814439368083686232, 8497321384591725159
Offset: 5
-
b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(5):
seq(a(n), n=5..30);
-
b[n_, k_, m_, l_] := b[n, k, m, l] = If[n < 1, 1, If[l - n > k, 0, b[n - 1, k, m + 1, n]] + m b[n - 1, k, m, l]];
A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
a[n_] := With[{k = 5}, A[n, k] - A[n, k - 1]];
a /@ Range[5, 30] (* Jean-François Alcover, May 05 2020, after Maple *)
A322879
Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals six.
Original entry on oeis.org
0, 1, 35, 413, 3709, 30396, 242366, 1934021, 15653524, 129267234, 1091892025, 9444993005, 83722879838, 760771479660, 7087056828919, 67674638461955, 662248199987728, 6638947646238102, 68153572265860585, 716151632403862252, 7699437833837232406
Offset: 6
-
b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(6):
seq(a(n), n=6..30);
A322880
Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals seven.
Original entry on oeis.org
0, 1, 67, 1059, 11373, 106256, 940608, 8193031, 71568443, 633413486, 5710573774, 52579554510, 494986212033, 4766754646529, 46966622143740, 473477764449909, 4883216510830794, 51513192445470426, 555667122424414886, 6127026713823497897, 69034256792655555566
Offset: 7
-
b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(7):
seq(a(n), n=7..30);
A322881
Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals eight.
Original entry on oeis.org
0, 1, 131, 2837, 36733, 392532, 3862958, 36745885, 346270455, 3276723147, 31384368348, 305668217577, 3035028866706, 30761374688048, 318435571825333, 3367380704425616, 36376061350280633, 401367264163810215, 4522617803400779891, 52030240381937090624
Offset: 8
-
b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(8):
seq(a(n), n=8..30);
A322882
Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals nine.
Original entry on oeis.org
0, 1, 259, 7851, 123693, 1517480, 16628928, 172861375, 1757583339, 17780116911, 180778826049, 1858914009077, 19407229306905, 206203531592425, 2232778235440364, 24655217395787251, 277719538910592762, 3191229583066629810, 37404691679158439649
Offset: 9
-
b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(9):
seq(a(n), n=9..30);
A322883
Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals ten.
Original entry on oeis.org
0, 1, 515, 22253, 430909, 6094476, 74507486, 847129333, 9296465127, 100540964675, 1085004090887, 11775039127122, 129155075413877, 1436488582202316, 16235344928131625, 186710546094489052, 2186538096666720967, 26085011069325363939, 317049671003606985326
Offset: 10
-
b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(10):
seq(a(n), n=10..30);
A322884
Number of set partitions of [2n] such that the maximal absolute difference between the least elements of consecutive blocks equals n.
Original entry on oeis.org
1, 1, 5, 39, 493, 9320, 242366, 8193031, 346270455, 17780116911, 1085004090887, 77324278953174, 6344818280326312, 592415284729545433, 62319734032202722887, 7323734663214254662683, 954467851066831095051393, 137065739258353347820981920
Offset: 0
a(1) = 1: 1|2.
a(2) = 5: 124|3, 12|34, 12|3|4, 13|2|4, 1|23|4.
-
b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> A(2*n, n)-`if`(n=0, 0, A(2*n, n-1)):
seq(a(n), n=0..20);
-
b[n_, k_, m_, l_] := b[n, k, m, l] = If[n < 1, 1, If[l - n > k, 0, b[n - 1, k, m + 1, n]] + m b[n - 1, k, m, l]];
A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
a[n_] := A[2 n, n] - If[n == 0, 0, A[2 n, n - 1]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jan 03 2019, translated from Maple *)
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