A081437 -id:A081437 - cp's OEIS frontend

A081436 Fifth subdiagonal in array of n-gonal numbers A081422.

1, 7, 24, 58, 115, 201, 322, 484, 693, 955, 1276, 1662, 2119, 2653, 3270, 3976, 4777, 5679, 6688, 7810, 9051, 10417, 11914, 13548, 15325, 17251, 19332, 21574, 23983, 26565, 29326, 32272, 35409, 38743, 42280, 46026, 49987, 54169, 58578, 63220

Offset: 0

Paul Barry, Mar 21 2003

One of a family of sequences with palindromic generators.
Also as A(n) = (1/6)*(6*n^3 - 3*n^2 + 3*n), n>0: structured pentagonal diamond numbers (vertex structure 5). (Cf. A004068 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers.) - James A. Record (james.record(AT)gmail.com), Nov 07 2004
Sequence of the absolute values of the z^1 coefficients of the polynomials in the GF4 denominators of A156933. See A157705 for background information. - Johannes W. Meijer, Mar 07 2009
Row 1 of the convolution arrays A213831 and A213833. - Clark Kimberling, Jul 04 2012
Partial sums of A056109. - J. M. Bergot, Jun 22 2013
Number of ordered pairs of intersecting multisets of size 2, each chosen with repetition from {1,...,n}. - Robin Whitty, Feb 12 2014
Row sums of A244418. - L. Edson Jeffery, Jan 10 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Christian Barrientos, The number of spanning trees of cyclic snakes, Indones. J. Comb. (2025) Vol. 9, No. 1, 21-30. See p. 29.
J. A. Dias da Silva and Pedro J. Freitas, Counting Spectral Radii of Matrices with Positive Entries, arXiv:1305.1139 [math.CO], 2013.
Theorem of the Day, Lovász Local Lemma example involving intersecting pairs of multisets
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A081434, A081435, A081437, A156933, A157705, A244418.

List([0..40], n-> (n+1)*(2*(n+1)^2-n)/2); # G. C. Greubel, Aug 14 2019

[(2*n^3+5*n^2+5*n+2)/2: n in [0..40]]; // Vincenzo Librandi, Jul 19 2011

A081436 := proc(n)
    (n+1)*(2*n^2+3*n+2)/2 ;
end proc:
seq(A081436(n),n=0..60) ; # R. J. Mathar, Jun 26 2013

LinearRecurrence[{4, -6, 4, -1}, {1, 7, 24, 58}, 40] (* Jean-François Alcover, Sep 21 2017 *)

a(n)=n^3+5/2*n*(n+1)+1 \\ Charles R Greathouse IV, Jun 20 2013

[(n+1)*(2*(n+1)^2-n)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019

a(n) = (n+1)*(2*n^2 + 3*n + 2)/2.
G.f.: (1+x)*(1+2*x)/(1-x)^4. (Convolution of A005408 and A016777.)
a(n) = A110449(n, n-1), for n>1.
a(n) = (n+1)*T(n+1) + n*T(n), where T( ) are triangular numbers. Binomial transform of [1, 6, 11, 6, 0, 0, 0, ...]. - Gary W. Adamson, Dec 28 2007
E.g.f.: exp(x)*(2 + 12*x + 11*x^2 + 2*x^3)/2. - Stefano Spezia, Apr 13 2021
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Apr 14 2021

G.f. simplified and crossrefs added by Johannes W. Meijer, Mar 07 2009

A143326 Table T(n,k) by antidiagonals. T(n,k) is the number of primitive (=aperiodic) k-ary words with length less than or equal to n (n,k >= 1).

Original entry on oeis.org

1, 2, 1, 3, 4, 1, 4, 9, 10, 1, 5, 16, 33, 22, 1, 6, 25, 76, 105, 52, 1, 7, 36, 145, 316, 345, 106, 1, 8, 49, 246, 745, 1336, 1041, 232, 1, 9, 64, 385, 1506, 3865, 5356, 3225, 472, 1, 10, 81, 568, 2737, 9276, 19345, 21736, 9705, 976, 1, 11, 100, 801, 4600, 19537, 55686

Offset: 1

Alois P. Heinz, Aug 07 2008

The coefficients of the polynomial of row n are given by the n-th row of triangle A134541; for example row 4 has polynomial -k+k^3+k^4.

			T(2,3) = 9, because there are 9 primitive words of length less than or equal to 2 over 3-letter alphabet {a,b,c}: a, b, c, ab, ac, ba, bc, ca, cb; note that the non-primitive words aa, bb and cc don't belong to the list; secondly note that the words in the list need not be Lyndon words, for example ba can be derived from ab by a cyclic rotation of the positions.
Table begins:
  1,   2,    3,     4,      5,       6,       7,        8, ...
  1,   4,    9,    16,     25,      36,      49,       64, ...
  1,  10,   33,    76,    145,     246,     385,      568, ...
  1,  22,  105,   316,    745,    1506,    2737,     4600, ...
  1,  52,  345,  1336,   3865,    9276,   19537,    37360, ...
  1, 106, 1041,  5356,  19345,   55686,  136801,   298936, ...
  1, 232, 3225, 21736,  97465,  335616,  960337,  2396080, ...
  1, 472, 9705, 87016, 487465, 2013936, 6722737, 19169200, ...
  ...
From _Wolfdieter Lang_, Feb 01 2014: (Start)
The triangle Tri(n,m) := T(m,n-(m-1)) begins:
n\m  1   2    3     4     5      6      7     8    9  10 ...
1:   1
2:   2   1
3:   3   4    1
4:   4   9   10     1
5:   5  16   33    22     1
6:   6  25   76   105    52      1
7:   7  36  145   316   345    106      1
8:   8  49  246   745  1336   1041    232     1
9:   9  64  385  1506  3865   5356   3225   472    1
10: 10  81  568  2737  9276  19345  21736  9705  976   1
...
For the columns see A000027, A000290, A081437, ... (End)

Alois P. Heinz, Antidiagonals n = 1..141, flattened
Index entries for sequences related to Lyndon words

Column 1: A000012. Rows 1-3: A000027, A000290, A081437 and A085490. See also A143324, A143327, A134541, A008683.

with(numtheory):
f0:= proc(n) option remember;
       unapply(k^n-add(f0(d)(k), d=divisors(n) minus {n}), k)
     end:
g0:= proc(n) option remember; unapply(add(f0(j)(x), j=1..n), x) end:
T:= (n, k)-> g0(n)(k):
seq(seq(T(n, 1+d-n), n=1..d), d=1..12);

f0[n_] := f0[n] = Function[k, k^n-Sum[f0[d][k], {d, Divisors[n] // Most}]]; g0[n_] := g0[n] = Function[x, Sum[f0[j][x], {j, 1, n}]]; T[n_, k_] := g0[n][k]; Table[T[n, 1+d-n], {d, 1, 12}, {n, 1, d}]//Flatten (* Jean-François Alcover, Feb 12 2014, translated from Maple *)

T(n,k) = Sum_{1<=j<=n} Sum_{d|j} k^d * mu(j/d).
T(n,k) = Sum_{1<=j<=n} A143324(j,k).
T(n,k) = A143327(n,k) * k.

A144390 a(n) = 3*n^2 - n - 1.

Original entry on oeis.org

1, 9, 23, 43, 69, 101, 139, 183, 233, 289, 351, 419, 493, 573, 659, 751, 849, 953, 1063, 1179, 1301, 1429, 1563, 1703, 1849, 2001, 2159, 2323, 2493, 2669, 2851, 3039, 3233, 3433, 3639, 3851, 4069, 4293, 4523, 4759, 5001, 5249, 5503, 5763, 6029, 6301, 6579

Offset: 1

Paul Curtz, Oct 02 2008

Sequence's original Name was "First bisection of A135370."

The partial sums of this sequence give A081437. - Leo Tavares, Dec 26 2021

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
John Elias, Illustration: Belted Hexagrams
Leo Tavares, Illustration: Bounded Hexagons
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A016933, A049450, A144391.
Cf. A003215, A005408, A016754, A002378.
Cf. A081437 (partial sums).

[3*n^2-n-1: n in [1..60]]; // Vincenzo Librandi, Jun 14 2011

A144390:=n->3*n^2-n-1; seq(A144390(n), n=1..50); # Wesley Ivan Hurt, Mar 26 2014

Table[3*n^2 -n -1 , {n,0,50}] (* G. C. Greubel, Jul 19 2017 *)

a(n)=3*n^2-n-1 \\ Charles R Greathouse IV, Oct 07 2015

a(n+1) = a(n) + 6*n + 2; see A016933.
G.f.: x*(1+6*x-x^2)/(1-x)^3. a(n) = A049450(n)-1. - R. J. Mathar, Oct 24 2008
a(-n) = A144391(n). - Michael Somos, Mar 27 2014
E.g.f.: (3*x^2 + 2*x -1)*exp(x) + 1. - G. C. Greubel, Jul 19 2017
From Leo Tavares, Dec 26 2021: (Start)
a(n) = A003215(n) - 2*A005408(n). See Bounded Hexagons illustration.
a(n) = A016754(n-1) - A002378(n-2). (End)
a(n) = A003154(n) - A049451(n-1). - John Elias, Dec 22 2022

Edited by R. J. Mathar, Oct 24 2008

More terms from Vladimir Joseph Stephan Orlovsky, Oct 25 2008

A081422 Triangle read by rows in which row n consists of the first n+1 n-gonal numbers.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 1, 3, 6, 10, 1, 4, 9, 16, 25, 1, 5, 12, 22, 35, 51, 1, 6, 15, 28, 45, 66, 91, 1, 7, 18, 34, 55, 81, 112, 148, 1, 8, 21, 40, 65, 96, 133, 176, 225, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451

Offset: 0

Paul Barry, Mar 21 2003

			The array starts
  1  1  3 10 ...
  1  2  6 16 ...
  1  3  9 22 ...
  1  4 12 28 ...
The triangle starts
  1;
  1,  1;
  1,  2,  3;
  1,  3,  6, 10;
  1,  4,  9, 16, 25;
  ...

T. D. Noe, Rows n = 0..100 of triangle, flattened
Eric Weisstein's World of Mathematics, Polygonal Number

Rows include A060354, A064808, A006000, A006003, A002411.
Diagonals include A001093, A053698, A069778, A000578, A002414, A081423, A081435, A081436, A081437, A081438, A081441.
Antidiagonals are composed of n-gonal numbers.

Flat(List([0..10], n-> List([1..n+1], k-> k*((n-2)*k-(n-4))/2 ))); # G. C. Greubel, Aug 14 2019

[[k*((n-2)*k-(n-4))/2: k in [1..n+1]]: n in [0..10]]; // G. C. Greubel, Oct 13 2018

Table[PolygonalNumber[n,i],{n,0,10},{i,n+1}]//Flatten (* Requires Mathematica version 10.4 or later *) (* Harvey P. Dale, Aug 27 2016 *)

tabl(nn) = {for (n=0, nn, for (k=1, n+1, print1(k*((n-2)*k-(n-4))/2, ", ");); print(););} \\ Michel Marcus, Jun 22 2015

[[k*((n-2)*k -(n-4))/2 for k in (1..n+1)] for n in (0..10)] # G. C. Greubel, Aug 14 2019

Array of coefficients of x in the expansions of T(k, x) = (1 + k*x -(k-2)*x^2)/(1-x)^4, k > -4.

T(n, k) = k*((n-2)*k -(n-4))/2 (see MathWorld link). - Michel Marcus, Jun 22 2015

A081435 Diagonal in array of n-gonal numbers A081422.

Original entry on oeis.org

1, 5, 18, 46, 95, 171, 280, 428, 621, 865, 1166, 1530, 1963, 2471, 3060, 3736, 4505, 5373, 6346, 7430, 8631, 9955, 11408, 12996, 14725, 16601, 18630, 20818, 23171, 25695, 28396, 31280, 34353, 37621, 41090, 44766, 48655, 52763, 57096, 61660

Offset: 0

Paul Barry, Mar 21 2003

One of a family of sequences with palindromic generators.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A081434, A081436, A081437.

List([0..40], n-> (n+1)*(2*(n+1)^2-3*n)/2); # G. C. Greubel, Aug 14 2019

[(2*n^3+3*n^2+3*n+2)/2: n in [0..40]]; // Vincenzo Librandi, Aug 08 2013

a := n-> (n+1)*(2*(n+1)^2-3*n)/2; seq(a(n), n = 0..40); # G. C. Greubel, Aug 14 2019

Table[(n^3 +(n+1)^3 -1)/2 +1, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
CoefficientList[Series[(1 +3x^2 -4x^3)/(1-x)^5, {x,0,40}], x] (* Vincenzo Librandi, Aug 08 2013 *)
LinearRecurrence[{4,-6,4,-1},{1,5,18,46},40] (* Harvey P. Dale, Dec 28 2024 *)

vector(40, n, n--; (n+1)*(2*(n+1)^2-3*n)/2) \\ G. C. Greubel, Aug 14 2019

[(n+1)*(2*(n+1)^2-3*n)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019

a(n) = (2*n^3 +3*n^2 +3*n +2)/2.
G.f.: (1 +3*x^2 -4*x^3)/(1-x)^5.
E.g.f.: (2 +8*x +9*x^2 +2*x^3)*exp(x)/2. - G. C. Greubel, Aug 14 2019

A153257 a(n) = n^3 - (n+1)^2.

Original entry on oeis.org

-1, -3, -1, 11, 39, 89, 167, 279, 431, 629, 879, 1187, 1559, 2001, 2519, 3119, 3807, 4589, 5471, 6459, 7559, 8777, 10119, 11591, 13199, 14949, 16847, 18899, 21111, 23489, 26039, 28767, 31679, 34781, 38079, 41579, 45287, 49209, 53351, 57719, 62319, 67157, 72239

Offset: 0

Vladimir Joseph Stephan Orlovsky, Dec 22 2008

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A045991, A069778, A081437, A140719.

Table[n^3-(n+1)^2,{n,0,40}] (* Harvey P. Dale, Oct 05 2022 *)

my(x='x+O('x^43)); Vec((x^3+5*x^2+x-1)/(x-1)^4) \\ Elmo R. Oliveira, Aug 27 2025

From Elmo R. Oliveira, Aug 27 2025: (Start)
G.f.: (-1 + x + 5*x^2 + x^3)/(1 - x)^4.
E.g.f.: (-1 + x)*(1 + 3*x + x^2)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

More terms from Elmo R. Oliveira, Aug 27 2025

A081438 Diagonal in array of n-gonal numbers A081422.

Original entry on oeis.org

1, 11, 36, 82, 155, 261, 406, 596, 837, 1135, 1496, 1926, 2431, 3017, 3690, 4456, 5321, 6291, 7372, 8570, 9891, 11341, 12926, 14652, 16525, 18551, 20736, 23086, 25607, 28305, 31186, 34256, 37521, 40987, 44660, 48546, 52651, 56981, 61542, 66340

Offset: 0

Paul Barry, Mar 21 2003

One of a family of sequences with palindromic generators.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A081436, A081437, A081441, A177058.

List([0..45], n-> (2*n^3+9*n^2+9*n+2)/2); # G. C. Greubel, Aug 14 2019

[(2*n^3+9*n^2+9*n+2)/2: n in [0..45]]; // Vincenzo Librandi, Aug 08 2013

seq((2*n^3+9*n^2+9*n+2)/2, n=0..45); # G. C. Greubel, Aug 14 2019

CoefficientList[Series[(1 +6x -9x^2 +2x^3)/(1-x)^5, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 08 2013 *)
LinearRecurrence[{4,-6,4,-1},{1,11,36,82},50] (* Harvey P. Dale, Jan 20 2022 *)

vector(45, n, n--; (2*n^3+9*n^2+9*n+2)/2) \\ G. C. Greubel, Aug 14 2019

[(2*n^3+9*n^2+9*n+2)/2 for n in (0..45)] # G. C. Greubel, Aug 14 2019

a(n) = (2*n^3+9*n^2+9*n+2)/2.
G.f.: (1+6*x-9*x^2+2*x^3)/(1-x)^5.
From Bruno Berselli, Jun 04 2010: (Start)
G.f.: (1+7*x-2*x^2)/(1-x)^4 (simplified).
a(n) = (n+1)*(2*n^2+7*n+2)/2.
a(n) -4*a(n-1) +6*a(n-2) -4*a(n-3) +a(n-4) = 0, with n>3.
a(n) = (A177058(n+3) + A177058(n+2))/2. (End)
E.g.f.: (1/2)*exp(x)*(2 +20*x + 15*x^2 + 2*x^3). - Stefano Spezia, Aug 15 2019

A085490 Number of pairs with two different elements which can be obtained by selecting unique elements from two sets with n+1 and n^2 elements respectively and n common elements.

Original entry on oeis.org

0, 1, 10, 33, 76, 145, 246, 385, 568, 801, 1090, 1441, 1860, 2353, 2926, 3585, 4336, 5185, 6138, 7201, 8380, 9681, 11110, 12673, 14376, 16225, 18226, 20385, 22708, 25201, 27870, 30721, 33760, 36993, 40426, 44065, 47916, 51985, 56278, 60801, 65560, 70561, 75810, 81313

Offset: 0

Polina S. Dolmatova (polinasport(AT)mail.ru), Aug 15 2003

			a(2) = 10 because we can write a(2) = 2^3 + 2^2 - 2 = 10.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A270109.

[n^3+n^2-n: n in [0..50]]; // Vincenzo Librandi, Jun 22 2017

a:=n->sum(n*k, k=0..n):seq(a(n)+sum(n*k, k=2..n), n=0..30); # Zerinvary Lajos, Jun 10 2008
a:=n->sum(-2+sum(2+sum(2, j=1..n),j=1..n),j=1..n):seq(a(n)/2,n=0..40);# Zerinvary Lajos, Dec 06 2008
seq(n^3+n^2-n, n=0..100); # Robert Israel, Dec 05 2014

LinearRecurrence[{4, -6, 4, -1}, {0, 1, 10, 33}, 60] (* Vincenzo Librandi, Jun 22 2017 *)

a(n) = n^3 + n^2 - n = n*A028387(n-1).
a(n) = A081437(n-1), n>0. - R. J. Mathar, Sep 12 2008
G.f.: x*(1+6*x-x^2)/(1-x)^4. - Robert Israel, Dec 05 2014
E.g.f.: x*(1+4*x+x^2)*exp(x). - Robert Israel, Dec 05 2014
For q a prime power, a(q) is the number of pairs of commuting nilpotent 2*2 matrices with coefficients in GL(q). (Proof: the zero matrix commutes with all q^2 nilpotent matrices, each of the remaining q^2-1 nilpotent matrices commutes with exactly q nilpotent matrices.) - Mark Wildon, Jun 18 2017

A081423 Subdiagonal of array of n-gonal numbers A081422.

Original entry on oeis.org

1, 3, 12, 34, 75, 141, 238, 372, 549, 775, 1056, 1398, 1807, 2289, 2850, 3496, 4233, 5067, 6004, 7050, 8211, 9493, 10902, 12444, 14125, 15951, 17928, 20062, 22359, 24825, 27466, 30288, 33297, 36499, 39900, 43506, 47323, 51357, 55614, 60100

Offset: 0

Paul Barry, Mar 21 2003

One of a family of sequences with palindromic generators.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A081435, A081436, A081437.

List([0..40], n-> (2*n^3+n^2+n+2)/2); # G. C. Greubel, Aug 14 2019

[(2*n^3+n^2+n+2)/2: n in [0..40]]; // Vincenzo Librandi, Aug 08 2013

a := n-> (2*n^3+n^2+n+2)/2; seq(a(n), n = 0..40); # G. C. Greubel, Aug 14 2019

CoefficientList[Series[(1 -2x +7x^2 -6x^3)/(1-x)^5, {x,0,40}], x] (* Vincenzo Librandi, Aug 08 2013 *)

vector(40, n, n--; (2*n^3+n^2+n+2)/2) \\ G. C. Greubel, Aug 14 2019

[(2*n^3+n^2+n+2)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019

a(n) = (2*n^3 + n^2 + n + 2)/2.
G.f.: (1 -2*x +7*x^2 -6*x^3)/(1-x)^5.
E.g.f.: (2 +4*x +7*x^2 +2*x^3)*exp(x)/2. - G. C. Greubel, Aug 14 2019

A256141 Square array read by antidiagonals upwards: T(n,k), n>=0, k>=0, in which row n lists the partial sums of the n-th row of the square array of A256140.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 5, 7, 9, 5, 1, 1, 6, 9, 16, 11, 6, 1, 1, 7, 11, 25, 19, 15, 7, 1, 1, 8, 13, 36, 29, 28, 19, 8, 1, 1, 9, 15, 49, 41, 45, 37, 27, 9, 1, 1, 10, 17, 64, 55, 66, 61, 64, 29, 10, 1, 1, 11, 19, 81, 71, 91, 91, 125, 67, 33, 11, 1, 1, 12, 21, 100, 89, 120, 127, 216, 129, 76, 37, 12, 1

Offset: 0

Omar E. Pol, Mar 16 2015

Questions:
Is also A130667 a row of this square array?
Is also A116522 a row of this square array?
Is also A116526 a row of this square array?
Is also A116525 a row of this square array?
Is also A116524 a row of this square array?

			The corner of the square array with the first 15 terms of the first 12 rows looks like this:
--------------------------------------------------------------------------
A000012: 1, 1, 1,  1,  1,  1,  1,   1,   1,   1,   1,   1,   1,   1,   1
A000027: 1, 2, 3,  4,  5,  6,  7,   8,   9,  10,  11,  12,  13,  14,  15
A006046: 1, 3, 5,  9, 11, 15, 19,  27,  29,  33,  37,  45,  49,  57,  65
A130665: 1, 4, 7, 16, 19, 28, 37,  64,  67,  76,  85, 112, 121, 148, 175
A116520: 1, 5, 9, 25, 29, 45, 61, 125, 129, 145, 161, 225, 241, 305, 369
A130667? 1, 6,11, 36, 41, 66, 91, 216, 221, 246, 271, 396, 421, 546, 671
A116522? 1, 7,13, 49, 55, 91,127, 343, 349, 385, 421, 637, 673, 889,1105
A161342: 1, 8,15, 64, 71,120,169, 512, 519, 568, 617, 960,1009,1352,1695
A116526? 1, 9,17, 81, 89,153,217, 729, 737, 801, 865,1377,1441,1953,2465
.......: 1,10,19,100,109,190,271,1000,1009,1090,1171,1900,1981,2710,3439
A116525? 1,11,21,121,131,231,331,1331,1341,1441,1541,2541,2641,3641,4641
.......: 1,12,23,144,155,276,397,1728,1739,1860,1981,3312,3422,4764,6095

Index entries for sequences related to cellular automata

Cf. A000120, A255740, A255741, A256140.
First five rows are A000012, A000027, A006046, A130665, A116520. Row 7 is A161342.
First eight columns are A000012, A000027, A005408, A000290, A028387, A000384, A003215, A000578. Column 9 is A081437. Column 11 is A015237. Columns 13-15 are A005915, A005917, A000583.

cp's OEIS Frontend

A081436 Fifth subdiagonal in array of n-gonal numbers A081422.

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A143326 Table T(n,k) by antidiagonals. T(n,k) is the number of primitive (=aperiodic) k-ary words with length less than or equal to n (n,k >= 1).

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Maple

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A144390 a(n) = 3*n^2 - n - 1.

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A081422 Triangle read by rows in which row n consists of the first n+1 n-gonal numbers.

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A081435 Diagonal in array of n-gonal numbers A081422.

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A153257 a(n) = n^3 - (n+1)^2.

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