A001105 -id:A001105 - cp's OEIS frontend

A368522 Triangular array T, read by rows: T(n,k) = number of sums |x-y| + |y-z| - |x-z| = 2n-2-k, where x,y,z are in {1,2,...,n}.

1, 2, 6, 2, 8, 17, 2, 8, 18, 36, 2, 8, 18, 32, 65, 2, 8, 18, 32, 50, 106, 2, 8, 18, 32, 50, 72, 161, 2, 8, 18, 32, 50, 72, 98, 232, 2, 8, 18, 32, 50, 72, 98, 128, 321, 2, 8, 18, 32, 50, 72, 98, 128, 162, 430, 2, 8, 18, 32, 50, 72, 98, 128, 162, 200, 561, 2

Offset: 1

Clark Kimberling, Jan 25 2024

The rows are the reversals of the rows in A368521.

			First eight rows:
   1
   2   6
   2   8   17
   2   8   18   36
   2   8   18   32   65
   2   8   18   32   50   106
   2   8   18   32   50    72   161
   2   8   18   32   50    72    98    232
For n=2, there are 8 triples (x,y,z):
  111:  |x-y| + |y-z| - |x-z| = 0
  112:  |x-y| + |y-z| - |x-z| = 0
  121:  |x-y| + |y-z| - |x-z| = 2
  122:  |x-y| + |y-z| - |x-z| = 0
  211:  |x-y| + |y-z| - |x-z| = 0
  212:  |x-y| + |y-z| - |x-z| = 2
  221:  |x-y| + |y-z| - |x-z| = 0
  222:  |x-y| + |y-z| - |x-z| = 0
so row 2 of the array is (2,6), representing two 2s and six 0s.

Cf. A084990 (column 1), A000578 (row sums), A001105 (limiting row), A368521.

t[n_] := t[n] = Tuples[Range[n], 3]
a[n_, k_] := Select[t[n], Abs[#[[1]] - #[[2]]] + Abs[#[[2]] - #[[3]]]
 - Abs[#[[1]] - #[[3]]] ==  2n-2-k &]
u = Table[Length[a[n, k]], {n, 1, 15}, {k, 0, 2 n - 2, 2}]
v = Flatten[u] (* sequence *)
Column[Table[Length[a[n, k]], {n, 1, 15}, {k, 0, 2 n - 2, 2}]]  (* array *)

A141046 a(n) = 4*n^4.

Original entry on oeis.org

0, 4, 64, 324, 1024, 2500, 5184, 9604, 16384, 26244, 40000, 58564, 82944, 114244, 153664, 202500, 262144, 334084, 419904, 521284, 640000, 777924, 937024, 1119364, 1327104, 1562500, 1827904, 2125764, 2458624, 2829124, 3240000, 3694084, 4194304, 4743684, 5345344

Offset: 0

Fredrik Johansson, Jul 31 2008

Nonnegative integers a(n) such that (-a(n))^(1/4) is a Gaussian integer, since (n + n*i)^4 = -4*n^4
For n > 1, a(n) + k^4 is not prime for any k. - Derek Orr, May 31 2014
Suppose the vertices of a triangle are (T(n), T(n+j)), (T(n+2*j), T(n+3*j)) and (T(n+4*j), T(n+5*j)) where T(n) is the n-th triangular number. Then the area of this triangle will be a(j). - Charlie Marion, Mar 06 2021

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A000290, A000583, A001105, A005843, A008586.

a141046 = (* 4) . (^ 4)  -- Reinhard Zumkeller, Jan 25 2012

Mathematica
```
Table[4 n^4, {n, 0, 20}]
```

a(n)=4*n^4 \\ Charles R Greathouse IV, Jan 26 2012

a(n) = 4*n^4.
a(n) = A008586(A000583(n)) = A000290(A005843(A000290(n))). - Reinhard Zumkeller, Jan 25 2012
G.f.: 4*x*(1 + x)*(1 + 10*x + x^2)/(1 - x)^5. - Chai Wah Wu, Jun 22 2016
From G. C. Greubel, Jun 22 2016: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
E.g.f.: 4*x*(1 + 7*x + 6*x^2 + x^3)*exp(x). (End)
a(n) = A001105(n)^2. - Bruce J. Nicholson, Apr 03 2017
From Amiram Eldar, Jan 29 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^4/360.
Sum_{n>=1} (-1)^(n+1)/a(n) = 7*Pi^4/2880.
Product_{n>=1} (1 + 1/a(n)) = 2*cosh(Pi/2)^2/Pi^2.
Product_{n>=1} (1 - 1/a(n)) = 2*sin(Pi/sqrt(2))*sinh(Pi/sqrt(2))/Pi^2. (End)

A195321 a(n) = 18*n^2.

Original entry on oeis.org

0, 18, 72, 162, 288, 450, 648, 882, 1152, 1458, 1800, 2178, 2592, 3042, 3528, 4050, 4608, 5202, 5832, 6498, 7200, 7938, 8712, 9522, 10368, 11250, 12168, 13122, 14112, 15138, 16200, 17298, 18432, 19602, 20808, 22050, 23328, 24642, 25992, 27378, 28800, 30258, 31752

Offset: 0

Omar E. Pol, Sep 16 2011

Sequence found by reading the line from 0, in the direction 0, 18, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Semi-axis opposite to A195316 in the same spiral.
Area of a square with diagonal 6n. - Wesley Ivan Hurt, Jun 19 2014
Number of identical tessellation tiles that are composed of 48 equilateral edge joined triangles that can be formed into a order n hexagon. The example tiles shown in the link below are tessellated with eight sphinx tiles. See A291582. - Craig Knecht, Sep 02 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Craig Knecht, Hexagon tessellation.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Bisection of A195147.
Cf. A016802, A033581, A033583, A135453, A139098, A144555, A195322, A195323.
Cf. A000290, A001105, A008600, A016766, A033428, A195160, A195316, A291582.

[18*n^2:n in [0..40]]; // Vincenzo Librandi, Sep 20 2011

A195321:=n->18*n^2; seq(A195321(n), n=0..50); # Wesley Ivan Hurt, Jun 19 2014

18 Range[0, 50]^2 (* or *) CoefficientList[Series[18 x*(1 + x)/(1 - x)^3, {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 20 2014 *)
LinearRecurrence[{3,-3,1},{0,18,72},50] (* Harvey P. Dale, Mar 26 2023 *)

a(n)=18*n^2 \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 18*A000290(n) = 9*A001105(n) = 6*A033428(n) = 3*A033581(n) = 2*A016766(n).
G.f.: 18*x*(1+x)/(1-x)^3. - Wesley Ivan Hurt, Jun 20 2014
From Elmo R. Oliveira, Dec 01 2024: (Start)
E.g.f.: 18*x*(1 + x)*exp(x).
a(n) = n*A008600(n) = A195147(2*n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A195322 a(n) = 20*n^2.

Original entry on oeis.org

0, 20, 80, 180, 320, 500, 720, 980, 1280, 1620, 2000, 2420, 2880, 3380, 3920, 4500, 5120, 5780, 6480, 7220, 8000, 8820, 9680, 10580, 11520, 12500, 13520, 14580, 15680, 16820, 18000, 19220, 20480, 21780, 23120, 24500, 25920, 27380, 28880, 30420, 32000, 33620, 35280

Offset: 0

Omar E. Pol, Sep 16 2011

Sequence found by reading the line from 0, in the direction 0, 20, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Semiaxis opposite to A195317 in the same spiral.
a(n) is the sum of all the integers less than 10*n which are not multiple of 2 or 5. a(2) = (1 + 3 + 7 + 9) + (11 + 13 + 17 + 19) = 20 + 60 = 80 = 20 * 2^2. (Link Crux Mathematicorum). - Bernard Schott, May 15 2017
Number of terms less than 10^k (k=0, 1, 2, ...): 1, 1, 3, 8, 23, 71, 224, 708, 2237, 7072, 22361, 70711, ... - Muniru A Asiru, Feb 01 2018

			From _Muniru A Asiru_, Feb 01 2018: (Start)
n=0, a(0) = 20*0^2 = 0.
n=1, a(1) = 20*1^2 = 20.
n=1, a(2) = 20*2^2 = 80.
n=1, a(3) = 20*3^2 = 180.
n=1, a(4) = 20*4^2 = 320.
...
(End)

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Léo Sauvé, Problem 53, Crux Mathematicorum, Vol. 1, Nov. 1975, page 88.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Bisection of A195148.
Cf. A016802, A033581, A033583, A135453, A139098, A144555, A195321, A195323.
Cf. A000290, A001105, A005899, A010014, A016742, A033429, A195162, A195317.
Cf. A008602.

List([0..10^3],n->20*n^2); # Muniru A Asiru, Feb 01 2018

[20*n^2: n in [0..40]]; // Vincenzo Librandi, Sep 20 2011

a := n -> 20*n^2; seq(a(n), n=0..10^3); # Muniru A Asiru, Feb 01 2018

20 Range[0, 40]^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 20, 80}, 50] (* Harvey P. Dale, Jan 18 2013 *)

a(n) = 20*n^2 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 20*A000290(n) = 10*A001105(n) = 5*A016742(n) = 4*A033429(n) = 2*A033583(n).
a(0)=0, a(1)=20, a(2)=80; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jan 18 2013
a(n) = A010014(n) - A005899(n) for n > 0. - R. J. Cano, Sep 29 2015
From Elmo R. Oliveira, Nov 30 2024: (Start)
G.f.: 20*x*(1 + x)/(1-x)^3.
E.g.f.: 20*x*(1 + x)*exp(x).
a(n) = n*A008602(n) = A195148(2*n). (End)

A247375 Numbers m such that floor(m/2) is a square.

Original entry on oeis.org

0, 1, 2, 3, 8, 9, 18, 19, 32, 33, 50, 51, 72, 73, 98, 99, 128, 129, 162, 163, 200, 201, 242, 243, 288, 289, 338, 339, 392, 393, 450, 451, 512, 513, 578, 579, 648, 649, 722, 723, 800, 801, 882, 883, 968, 969, 1058, 1059, 1152, 1153, 1250, 1251, 1352, 1353

Offset: 0

Bruno Berselli, Sep 15 2014

Union of A001105 and A058331.

Squares of the sequence are listed in A055792.

Jens Kruse Andersen, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A001105, A055792, A058331, A213037.

Cf. A130404 (numbers m such that floor(m/2) is a triangular number).

[n: n in [0..1400] | IsSquare(Floor(n div 2))];

Select[Range[0, 1400], IntegerQ[Sqrt[Floor[#/2]]] &]
LinearRecurrence[{1,2,-2,-1,1},{0,1,2,3,8},70] (* Harvey P. Dale, Oct 21 2021 *)

[n for n in [0..1400] if is_square(floor(n/2))]

G.f.: x*( 1 + x - x^2 + 3*x^3 ) / ( (1 - x)^3*(1 + x)^2 ).
a(n) = 1 + ( 2*n*(n-1) + (2*n-3)*(-1)^n - 1 )/4.
a(n+1) = 1 + A213037(n).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n >= 5. - Wesley Ivan Hurt, Dec 18 2020
Sum_{n>=1} 1/a(n) = Pi^2/12 + coth(Pi/sqrt(2))*Pi/(2*sqrt(2)) + 1/2. - Amiram Eldar, Sep 24 2022

A277701 Positions of ones in A264977; positions of twos in A277330.

Original entry on oeis.org

1, 5, 13, 29, 41, 61, 85, 125, 173, 209, 253, 281, 313, 349, 421, 509, 565, 629, 701, 845, 929, 1021, 1133, 1261, 1405, 1693, 1861, 2045, 2269, 2525, 2665, 2813, 3121, 3313, 3389, 3725, 3905, 4093, 4541, 4841, 5053, 5209, 5257, 5333, 5629, 5993, 6245, 6629, 6781, 7453, 7813, 8189, 8537, 9085, 9593, 9685, 9905, 10109, 10421, 10517, 10669, 10921

Offset: 1

Antti Karttunen, Oct 27 2016

nonn

Positions in A260443 of terms that are twice square (terms in A001105, although not all of them are present in A260443).

Antti Karttunen, Table of n, a(n) for n = 1..720

Row 1 of A277710.
Cf. A001105, A260443, A264977, A277330.
Cf. also A277712, A277713.

A277712(n) = 2*a(n) for all n >= 1.

A329604 Numbers k such that A156552(k) == 1 (mod 3); numbers k for which A156552(2*k) is a multiple of 3.

Original entry on oeis.org

2, 5, 8, 11, 15, 17, 18, 20, 23, 31, 32, 33, 41, 42, 44, 45, 47, 50, 51, 59, 60, 67, 68, 69, 72, 73, 77, 78, 80, 83, 92, 93, 97, 98, 99, 103, 109, 110, 114, 119, 123, 124, 125, 127, 128, 132, 135, 137, 141, 149, 153, 157, 161, 162, 164, 167, 168, 170, 174, 176, 177, 179, 180, 182, 188, 191, 197, 200, 201, 204, 207, 210, 211, 217, 219, 221, 222

Offset: 1

Antti Karttunen, Nov 21 2019

nonn

Even terms of A329609, divided by two.

Numbers k for which A156552(k) == 1 (mod 3). - Antti Karttunen, Feb 27 2020

Antti Karttunen, Table of n, a(n) for n = 1..20000

Sequence A329603 sorted into ascending order.
Positions of 1's in A329903 and in A332814.
Cf. A156552, A329609.
Cf. A001105 (subsequence apart from the initial 0).
Cf. A031368 (a subsequence of prime terms).
Cf. also A332812, A324814, A332821.

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
isA329604(n) = !(A156552(2*n)%3);

New primary definition added by Antti Karttunen, Mar 01 2020

A350838 Heinz numbers of partitions with no adjacent parts of quotient 2.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 64, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83

Offset: 1

Gus Wiseman, Jan 18 2022

nonn

Differs from A320340 in having 105: (4,3,2), 315: (4,3,2,2), 455: (6,4,3), etc.

The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers with no adjacent prime indices of quotient 1/2.

			The terms and their prime indices begin:
      1: {}            19: {8}             38: {1,8}
      2: {1}           20: {1,1,3}         39: {2,6}
      3: {2}           22: {1,5}           40: {1,1,1,3}
      4: {1,1}         23: {9}             41: {13}
      5: {3}           25: {3,3}           43: {14}
      7: {4}           26: {1,6}           44: {1,1,5}
      8: {1,1,1}       27: {2,2,2}         45: {2,2,3}
      9: {2,2}         28: {1,1,4}         46: {1,9}
     10: {1,3}         29: {10}            47: {15}
     11: {5}           31: {11}            49: {4,4}
     13: {6}           32: {1,1,1,1,1}     50: {1,3,3}
     14: {1,4}         33: {2,5}           51: {2,7}
     15: {2,3}         34: {1,7}           52: {1,1,6}
     16: {1,1,1,1}     35: {3,4}           53: {16}
     17: {7}           37: {12}            55: {3,5}

The version with quotients >= 2 is counted by A000929, sets A018819.
                           <= 2 is A342191, counted by A342094.
                           < 2 is counted by A342096, sets A045690.
                           > 2 is counted by A342098, sets A040039.
The sets version (subsets of prescribed maximum) is counted by A045691.
These partitions are counted by A350837.
The strict case is counted by A350840.
For differences instead of quotients we have A350842, strict A350844.
The complement is A350845, counted by A350846.
A000041 = integer partitions.
A000045 = sets containing n with all differences > 2.
A003114 = strict partitions with no successions, ranked by A325160.
A056239 adds up prime indices, row sums of A112798, counted by A001222.
A116931 = partitions with no successions, ranked by A319630.
A116932 = partitions with differences != 1 or 2, strict A025157.
A323092 = double-free integer partitions, ranked by A320340.
A350839 = partitions with gaps and conjugate gaps, ranked by A350841.
Cf. A000302, A001105, A003000, A018819, A094537, A120641, A154402, A319613, A323093, A337135, A342097, A342095.

primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
Select[Range[100],And@@Table[FreeQ[Divide@@@Partition[primeptn[#],2,1],2],{i,2,PrimeOmega[#]}]&]

A007607 Skip 1, take 2, skip 3, etc.

Original entry on oeis.org

2, 3, 7, 8, 9, 10, 16, 17, 18, 19, 20, 21, 29, 30, 31, 32, 33, 34, 35, 36, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130

Offset: 1

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Numbers k with the property that the smallest Dyck path of the symmetric representation of sigma(k) has a central peak. (Cf. A237593.) - Omar E. Pol, Aug 28 2018

Union of A317303 and A014105. - Omar E. Pol, Aug 29 2018

			From _Omar E. Pol_, Aug 29 2018: (Start)
Written as an irregular triangle in which the row lengths are the nonzero even numbers the sequence begins:
    2,   3;
    7,   8,   9,  10;
   16,  17,  18,  19,  20,  21;
   29,  30,  31,  32,  33,  34,  35,  36;
   46,  47,  48,  49,  50,  51,  52,  53,  54,  55;
   67,  68,  69,  70,  71,  72,  73,  74,  75,  76,  77,  78;
   92,  93,  94,  95,  96,  97,  98,  99, 100, 101, 102, 103, 104, 105;
  121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136;
...
Row sums give the nonzero terms of A317297.
Column 1 gives A130883, n >= 1.
Right border gives A014105, n >= 1.
(End)

R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 177.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A063656, A004202, A063657, A007606, A064801, A004202.
Complement of A007606.
Cf. A014105, A130883, A317297.
Similar to A360418.

a007607 n = a007607_list !! (n-1)
a007607_list = skipTake 1 [1..] where
   skipTake k xs = take (k + 1) (drop k xs)
                   ++ skipTake (k + 2) (drop (2*k + 1) xs)
-- Reinhard Zumkeller, Feb 12 2011

a007607_list' = f $ tail $ scanl (+) 0 [1..] where
   f (t:t':t'':ts) = [t+1..t'] ++ f (t'':ts)
-- Reinhard Zumkeller, Feb 12 2011

Flatten[ Table[i, {j, 2, 16, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (* Robert G. Wilson v, Mar 11 2004 *)
With[{t=20},Flatten[Take[TakeList[Range[(t(t+1))/2],Range[t]],{2,-1,2}]]] (* Harvey P. Dale, Sep 26 2021 *)

for(m=0,10,for(n=2*m^2+3*m+2,2*m^2+5*m+3,print1(n", "))) \\ Charles R Greathouse IV, Feb 12 2011

G.f.: 1/(1-x) * (1/(1-x) + x*Sum_{k>=1} (2k+1)*x^(k*(k+1))). - Ralf Stephan, Mar 03 2004
a(A000290(n)) = A001105(n). - Reinhard Zumkeller, Feb 12 2011
A057211(a(n)) = 0. - Reinhard Zumkeller, Dec 30 2011
a(n) = floor(sqrt(n) + 1/2)^2 + n = A053187(n) + n. - Ridouane Oudra, May 04 2019

A067051 The smallest k>1 such that k divides sigma(k*n) is equal to 3.

Original entry on oeis.org

2, 8, 18, 32, 49, 50, 72, 98, 128, 162, 169, 196, 200, 242, 288, 338, 361, 392, 441, 450, 512, 578, 648, 676, 722, 784, 800, 882, 961, 968, 1058, 1152, 1225, 1250, 1352, 1369, 1444, 1458, 1521, 1568, 1682, 1764, 1800, 1849, 1922, 2048, 2178, 2312, 2450, 2592

Offset: 1

Benoit Cloitre, Jul 26 2002

The smallest m>1 such that m divides sigma(m*n) is 2, 3 or 6.
Appears to be the same sequence as A074629. - Ralf Stephan, Aug 18 2004. [Proof: Mathar link]
Square terms are in A074216. Nonsquare terms appear to be A001105 except {0}. - Michel Marcus, Dec 26 2013

Amiram Eldar, Table of n, a(n) for n = 1..10000
R. J. Mathar, OEIS A074629

Subsequence of A087943.

Cf. A072862, A074384, A074627, A074628, A074630.

[n: n in [1..3*10^3] | (SumOfDivisors(n) mod 6) eq 3]; // Vincenzo Librandi, Dec 11 2015

select(t -> numtheory:-sigma(t) mod 6 = 3, [$1..10000]); # Robert Israel, Dec 11 2015

Select[Range@ 2600, Mod[DivisorSigma[1, #], 6] == 3 &] (* Michael De Vlieger, Dec 10 2015 *)

isok(n) = (sigma(2*n) % 2) && !(sigma(3*n) % 3); \\ Michel Marcus, Dec 26 2013

{n: A000203(n) mod 6 = 3.}  (Old definition of A074629) - Labos Elemer, Aug 26 2002
In the prime factorization of n, no odd prime has odd exponent, and 2 has odd exponent or at least one prime == 1 (mod 6) has exponent == 2 (mod 6). - Robert Israel, Dec 11 2015
{n: A049605(n) = 3}. - R. J. Mathar, May 19 2020
{n: A084301(n) = 3 }. - R. J. Mathar, May 19 2020
A087943 INTERSECT A028982. - R. J. Mathar, May 30 2020

cp's OEIS Frontend

A368522 Triangular array T, read by rows: T(n,k) = number of sums |x-y| + |y-z| - |x-z| = 2n-2-k, where x,y,z are in {1,2,...,n}.

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A141046 a(n) = 4*n^4.

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A195321 a(n) = 18*n^2.

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A195322 a(n) = 20*n^2.

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A247375 Numbers m such that floor(m/2) is a square.

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Magma

Mathematica

Sage

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A277701 Positions of ones in A264977; positions of twos in A277330.

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A329604 Numbers k such that A156552(k) == 1 (mod 3); numbers k for which A156552(2*k) is a multiple of 3.

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PARI

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