A001106 -id:A001106 - cp's OEIS frontend

A262000 a(n) = n^2(7n - 5)/2.

0, 1, 18, 72, 184, 375, 666, 1078, 1632, 2349, 3250, 4356, 5688, 7267, 9114, 11250, 13696, 16473, 19602, 23104, 27000, 31311, 36058, 41262, 46944, 53125, 59826, 67068, 74872, 83259, 92250, 101866, 112128, 123057, 134674, 147000, 160056, 173863, 188442, 203814, 220000

Offset: 0

Bruno Berselli, Sep 08 2015

Also, structured enneagonal prism numbers.

			For n=8, a(8) = 8*(7*0+1)+8*(7*1+1)+8*(7*2+1)+8*(7*3+1)+8*(7*4+1)+8*(7*5+1)+8*(7*6+1)+8*(7*7+1) = 1632.

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

Cf. similar sequences with the formula n^2*(k*n - k + 2)/2: A000290 (k=0), A002411 (k=1), A000578 (k=2), A050509 (k=3), A015237 (k=4), A006597 (k=5), A100176 (k=6), this sequence (k=7), A103532 (k=8).

Cf. A001106, A069125.

Magma
```
[n^2*(7*n-5)/2: n in [0..40]];
```

Table[n^2 (7 n - 5)/2, {n, 0, 40}]
LinearRecurrence[{4,-6,4,-1},{0,1,18,72},50] (* Harvey P. Dale, Oct 04 2016 *)

PARI
```
vector(40, n, n--; n^2*(7*n-5)/2)
```
Sage
```
[n^2*(7*n-5)/2 for n in (0..40)]
```

G.f.: x*(1 + 14*x + 6*x^2)/(1 - x)^4.
a(n) = Sum_{i=0..n-1} n*(7*i+1) for n>0, a(0)=0.
a(n+1) + a(-n) = A069125(n+1).
Sum_{i>0} 1/a(i) = 1.082675669875907610300284768825... = (42*(log(14) + 2*(cos(Pi/7)*log(cos(3*Pi/14)) + log(sin(Pi/7))*sin(Pi/14) - log(cos(Pi/14)) * sin(3*Pi/14))) + 21*Pi*tan(3*Pi/14))/75 - Pi^2/15. - Vaclav Kotesovec, Oct 04 2016
From Elmo R. Oliveira, Aug 06 2025: (Start)
E.g.f.: exp(x)*x*(2 + 16*x + 7*x^2)/2.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

A276682 Number of divisors of the n-th 9-gonal number.

Original entry on oeis.org

1, 3, 8, 4, 6, 4, 8, 12, 6, 6, 18, 8, 4, 8, 16, 8, 8, 9, 14, 24, 8, 4, 16, 12, 8, 8, 24, 8, 12, 12, 8, 20, 8, 4, 48, 24, 4, 12, 16, 24, 8, 12, 12, 16, 18, 4, 20, 16, 9, 16, 40, 8, 8, 8, 24, 36, 8, 4, 24, 24, 4, 16, 24, 12, 24, 8, 16, 16, 8, 12, 16, 18, 8, 16

Offset: 1

Colin Barker, Sep 13 2016

nonn

			a(2) = 3 because the 2nd 9-gonal number is 9, which has 3 divisors: 1,3,9.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A000005, A001106.

Cf. A063440 (m=3), A048691 (m=4), A276678 (m=5), A276679 (m=6), A276680 (m=7), A276681 (m=8), A276683 (m=10).

DivisorSigma[0,PolygonalNumber[9,Range[80]]] (* Harvey P. Dale, Dec 02 2024 *)

pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
vector(150, n, numdiv(pg(9,n)))

a(n) = A000005(A001106(n)).

A051877 Partial sums of A051740.

Original entry on oeis.org

1, 12, 57, 182, 462, 1008, 1974, 3564, 6039, 9724, 15015, 22386, 32396, 45696, 63036, 85272, 113373, 148428, 191653, 244398, 308154, 384560, 475410, 582660, 708435, 855036, 1024947, 1220842, 1445592, 1702272, 1994168, 2324784, 2697849, 3117324, 3587409

Offset: 0

Barry E. Williams, Dec 14 1999

Convolution of triangular numbers (A000217) and enneagonal numbers (A001106). - Bruno Berselli, Jul 21 2015

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index to sequences related to pyramidal numbers
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A051740; A000217, A001106.

Cf. A093564 ((7, 1) Pascal, column m=5).

List([0..40], n-> (7*n+5)*Binomial(n+4,4)/5); # G. C. Greubel, Aug 29 2019

[(n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120 : n in [0..40]]; // Wesley Ivan Hurt, May 02 2015

A051877:=n->binomial(n+4,4)*(7*n+5)/5: seq(A051877(n), n=0..40); # Wesley Ivan Hurt, May 02 2015

Table[(n+1)(n+2)(n+3)(n+4)(7n+5)/120, {n, 0, 40}] (* Vincenzo Librandi, May 03 2015 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{1,12,57,182,462,1008},40] (* Harvey P. Dale, May 05 2022 *)

vector(40, n, (7*n-2)*binomial(n+3,4)/5) \\ G. C. Greubel, Aug 29 2019

[(7*n+5)*binomial(n+4,4)/5 for n in (0..40)] # G. C. Greubel, Aug 29 2019

a(n) = C(n+4, 4)*(7*n+5)/5.
G.f.: (1+6*x)/(1-x)^6.
From Wesley Ivan Hurt, May 02 2015: (Start)
a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6).
a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120. (End)
E.g.f.: (5! +1320*x +2040*x^2 +920*x^3 +145*x^4 +7*x^5)*exp(x)/5!

A226489 a(n) = n(15n-11)/2.

Original entry on oeis.org

0, 2, 19, 51, 98, 160, 237, 329, 436, 558, 695, 847, 1014, 1196, 1393, 1605, 1832, 2074, 2331, 2603, 2890, 3192, 3509, 3841, 4188, 4550, 4927, 5319, 5726, 6148, 6585, 7037, 7504, 7986, 8483, 8995, 9522, 10064, 10621, 11193, 11780, 12382, 12999, 13631, 14278, 14940

Offset: 0

Bruno Berselli, Jun 09 2013

Sum of n-th 9-gonal (nonagonal) number and n-th 10-gonal (decagonal) number.

Sum of reciprocals of a(n), for n > 0: 0.614629940137818703272919217222307...

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A001106, A001107, A064761.

Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=15: see list in A226488.

Magma
```
[n*(15*n-11)/2: n in [0..50]];
```

I:=[0,2,19]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..45]]; // Vincenzo Librandi, Aug 18 2013

Table[n (15 n - 11)/2, {n, 0, 50}]
CoefficientList[Series[x (2 + 13 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)

a(n)=n*(15*n-11)/2 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: x*(2+13*x)/(1-x)^3.
a(n) + a(-n) = A064761(n).
From Elmo R. Oliveira, Jan 12 2025: (Start)
E.g.f.: exp(x)*x*(4 + 15*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A302913 Determinant of n X n matrix whose main diagonal consists of the first n 9-gonal numbers and all other elements are 1's.

Original entry on oeis.org

1, 8, 184, 8280, 612720, 67399200, 10312077600, 2093351752800, 544271455728000, 176343951655872000, 69655860904069440000, 32947222207624845120000, 18384549991854663576960000, 11949957494705531325024000000, 8950518163534442962442976000000

Offset: 1

Muniru A Asiru, Apr 15 2018

nonn

			The matrix begins:
1   1   1   1   1   1   1 ...
1   9   1   1   1   1   1 ...
1   1  24   1   1   1   1 ...
1   1   1  46   1   1   1 ...
1   1   1   1  75   1   1 ...
1   1   1   1   1 111   1 ...
1   1   1   1   1   1 154 ...

Cf. A001106 (nonagonal numbers).

Cf. Determinant of n X n matrix whose main diagonal consists of the first n k-gonal numbers and all other elements are 1's: A000142 (k=2), A067550 (k=3), A010791 (k=4, with offset 1), A302909 (k=5), A302910 (k=6), A302911 (k=7), A302912 (k=8), this sequence (k=9), A302914 (k=10).

d:=(i,j)->`if`(i<>j,1,i*(7*i-5)/2):
seq(LinearAlgebra[Determinant](Matrix(n,d)),n=1..16);

nmax = 20; Table[Det[Table[If[i == j, i*(7*i-5)/2, 1], {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* Vaclav Kotesovec, Apr 16 2018 *)
RecurrenceTable[{a[n+1] == a[n] * n*(7*n + 9)/2, a[1] == 1}, a, {n, 1, 20}] (* Vaclav Kotesovec, Apr 16 2018 *)
Table[FullSimplify[7^(n + 1) * Gamma[n] * Gamma[n + 9/7] / (9*Gamma[2/7]*2^n)], {n, 1, 15}] (* Vaclav Kotesovec, Apr 16 2018 *)

a(n) = matdet(matrix(n, n, i, j, if (i!=j, 1, i*(7*i-5)/2))); \\ Michel Marcus, Apr 16 2018

From Vaclav Kotesovec, Apr 16 2018: (Start)
a(n) = 7^(n+1) * Gamma(n) * Gamma(n + 9/7) / (9 * Gamma(2/7) * 2^n).
a(n) ~ Pi * 7^(n+1) * n^(2*n + 2/7) / (9 * Gamma(2/7) * 2^(n-1) * exp(2*n)).
a(n+1) = a(n) * n*(7*n + 9)/2.
(End)

A317302 Square array T(n,k) = (n - 2)(k - 1)k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 0, 1, 1, -3, 0, 1, 2, 0, -8, 0, 1, 3, 3, -2, -15, 0, 1, 4, 6, 4, -5, -24, 0, 1, 5, 9, 10, 5, -9, -35, 0, 1, 6, 12, 16, 15, 6, -14, -48, 0, 1, 7, 15, 22, 25, 21, 7, -20, -63, 0, 1, 8, 18, 28, 35, 36, 28, 8, -27, -80, 0, 1, 9, 21, 34, 45, 51, 49, 36, 9, -35, -99, 0, 1, 10, 24, 40, 55, 66

Offset: 0

Omar E. Pol, Aug 09 2018

Note that the formula gives several kinds of numbers, for example:
Row 0 gives 0 together with A258837.
Row 1 gives 0 together with A080956.
Row 2 gives A001477, the nonnegative numbers.
For n >= 3, row n gives the n-gonal numbers (see Crossrefs section).

			Array begins:
------------------------------------------------------------------------
n\k  Numbers       Seq. No.   0   1   2   3   4    5    6    7    8
------------------------------------------------------------------------
0    ............ (A258837):  0,  1,  0, -3, -8, -15, -24, -35, -48, ...
1    ............ (A080956):  0,  1,  1,  0, -2,  -5,  -9, -14, -20, ...
2    Nonnegatives  A001477:   0,  1,  2,  3,  4,   5,   6,   7,   8, ...
3    Triangulars   A000217:   0,  1,  3,  6, 10,  15,  21,  28,  36, ...
4    Squares       A000290:   0,  1,  4,  9, 16,  25,  36,  49,  64, ...
5    Pentagonals   A000326:   0,  1,  5, 12, 22,  35,  51,  70,  92, ...
6    Hexagonals    A000384:   0,  1,  6, 15, 28,  45,  66,  91, 120, ...
7    Heptagonals   A000566:   0,  1,  7, 18, 34,  55,  81, 112, 148, ...
8    Octagonals    A000567:   0,  1,  8, 21, 40,  65,  96, 133, 176, ...
9    9-gonals      A001106:   0,  1,  9, 24, 46,  75, 111, 154, 204, ...
10   10-gonals     A001107:   0,  1, 10, 27, 52,  85, 126, 175, 232, ...
11   11-gonals     A051682:   0,  1, 11, 30, 58,  95, 141, 196, 260, ...
12   12-gonals     A051624:   0,  1, 12, 33, 64, 105, 156, 217, 288, ...
13   13-gonals     A051865:   0,  1, 13, 36, 70, 115, 171, 238, 316, ...
14   14-gonals     A051866:   0,  1, 14, 39, 76, 125, 186, 259, 344, ...
15   15-gonals     A051867:   0,  1, 15, 42, 82, 135, 201, 280, 372, ...
...

Omar E. Pol, Polygonal numbers.
The OEIS, Polygonal numbers.
University of Surrey, Dept. of Mathematics, Polygonal Numbers - or Numbers as Shapes.
Eric Weisstein's World of Mathematics, Figurate Number.
Eric Weisstein's World of Mathematics, Polygonal Number.
Wikipedia, Polygonal number.
Index to sequences related to polygonal numbers

Column 0 gives A000004.
Column 1 gives A000012.
Column 2 gives A001477, which coincides with the row numbers.
Main diagonal gives A060354.
Row 0 gives 0 together with A258837.
Row 1 gives 0 together with A080956.
Row 2 gives A001477, the same as column 2.
For n >= 3, row n gives the n-gonal numbers: A000217 (n=3), A000290 (n=4), A000326 (n=5), A000384 (n=6), A000566 (n=7), A000567 (n=8), A001106 (n=9), A001107 (n=10), A051682 (n=11), A051624 (n=12), A051865 (n=13), A051866 (n=14), A051867 (n=15), A051868 (n=16), A051869 (n=17), A051870 (n=18), A051871 (n=19), A051872 (n=20), A051873 (n=21), A051874 (n=22), A051875 (n=23), A051876 (n=24), A255184 (n=25), A255185 (n=26), A255186 (n=27), A161935 (n=28), A255187 (n=29), A254474 (n=30).
Cf. A139600, A139601.
Cf. A303301 (similar table but with generalized polygonal numbers).

T(n,k) = A139600(n-2,k) if n >= 2.

T(n,k) = A139601(n-3,k) if n >= 3.

A033572 a(n) = (2n+1)(7*n+1).

Original entry on oeis.org

1, 24, 75, 154, 261, 396, 559, 750, 969, 1216, 1491, 1794, 2125, 2484, 2871, 3286, 3729, 4200, 4699, 5226, 5781, 6364, 6975, 7614, 8281, 8976, 9699, 10450, 11229, 12036, 12871, 13734, 14625, 15544, 16491, 17466, 18469, 19500, 20559, 21646, 22761, 23904, 25075, 26274, 27501, 28756

Offset: 0

N. J. A. Sloane

Sequence found by reading the line from 1, in the direction 1, 24,..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Also sequence found by reading the same line in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - Omar E. Pol, Sep 13 2011

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Bisection of A001106.

List([0..50], n-> (2*n+1)*(7*n+1)); # G. C. Greubel, Oct 12 2019

[(2*n+1)*(7*n+1): n in [0..50]]; // G. C. Greubel, Oct 12 2019

seq((2*n+1)*(7*n+1), n=0..50); # G. C. Greubel, Oct 12 2019

Table[(2*n+1)*(7*n+1), {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)
LinearRecurrence[{3,-3,1},{1,24,75},50] (* Harvey P. Dale, Apr 19 2023 *)

a(n)=(2*n+1)*(7*n+1) \\ Charles R Greathouse IV, Jun 17 2017

[(2*n+1)*(7*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019

a(n) = a(n-1) + 28*n - 5 for n>0, a(0)=1. - Vincenzo Librandi, Nov 17 2010
From G. C. Greubel, Oct 12 2019: (Start)
G.f.: (1 + 21*x + 6*x^2)/(1-x)^3.
E.g.f.: (1 + 23*x + 14*x^2)*exp(x). (End)
Sum 1/a(n) = -gamma/5 -2*log(2)/5 -psi(1/7)/5 = 1.0800940432405839438217..., gamma=A001620, psi(1/7) = -A354627. - R. J. Mathar, May 07 2024

A048909 9-gonal (or nonagonal) triangular numbers.

Original entry on oeis.org

1, 325, 82621, 20985481, 5330229625, 1353857339341, 343874433963061, 87342752369278225, 22184715227362706161, 5634830324997758086741, 1431224717834203191326125, 363525443499562612838749081, 92334031424171069457850940521, 23452480456295952079681300143325

Offset: 1

Eric W. Weisstein

We want solutions to m(7m-5)/2 = n(n+1)/2, or equivalently (14m-5)^2 = 7(2n+1)^2 + 18. This is the Pell-type equation x^2 - 7y^2 = 18.
This equation has unit solutions (x,y) = (5,1), (9, 3) and (19, 7), which lead to the family of solutions (5, 1), (9, 3), (19, 7), (61, 23), (135, 51), (299, 113), (971, 367), .... The corresponding integer solutions are (m,n) = (1,1), (10, 25), (154, 406), (2449, 6478), ... (A048907 and A048908), giving the nonagonal triangular numbers 1, 325, 82621, 20985481, ... shown here.
Also, numbers simultaneously 9-gonal and centered 9-gonal, the intersection of A001106 and A060544. - Steven Schlicker, Apr 24 2007

Colin Barker, Table of n, a(n) for n = 1..416
S. C. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, Mathematics Magazine, Vol. 84, No. 5, December 2011, pp. 339-350.
Eric Weisstein's World of Mathematics, Nonagonal Triangular Number.
Index entries for linear recurrences with constant coefficients, signature (255,-255,1).

Cf. A001106, A060544, A048907, A048908.

CP := n -> 1+1/2*9*(n^2-n): N:=10: u:=8: v:=1: x:=9: y:=1: k_pcp:=[1]: for i from 1 to N do tempx:=x; tempy:=y; x:=tempx*u+63*tempy*v: y:=tempx*v+tempy*u: s:=(y+1)/2: k_pcp:=[op(k_pcp),CP(s)]: end do: k_pcp; # Steven Schlicker, Apr 24 2007

LinearRecurrence[{255, -255, 1}, {1, 325, 82621}, 12]; (* Ant King, Nov 03 2011 *)

Vec(-x*(x^2+70*x+1)/((x-1)*(x^2-254*x+1)) + O(x^20)) \\ Colin Barker, Jun 22 2015

Define x(n) + y(n)*sqrt(63) = (9+sqrt(63))*(8+sqrt(63))^n, s(n) = (y(n)+1)/2; then a(n) = (2+9*(s(n)^2-s(n)))/2. - Steven Schlicker, Apr 24 2007
a(n+1) = 254*a(n+1)-a(n)+72. - Richard Choulet, Sep 22 2007
a(n+1) = 127*a(n+1)+36+6*(448*a(n)^2+256*a(n)+25)^0.5. - Richard Choulet, Sep 22 2007
G.f.: z*(1+70*z+z^2)/((1-z)*(1-254*z+z^2)). - Richard Choulet, Sep 22 2007
From Ant King, Nov 03 2011: (Start)
a(n) = 255*a(n-1) - 255*a(n-2) + a(n-3).
a(n) = 1/112*(9*(8 + 3*sqrt(7))^(2n-1) + 9*(8-3* sqrt(7))^(2n-1) - 32).
a(n) = floor(9/112*(8 + 3*sqrt(7))^(2n-1)).
Limit_{n -> oo} a(n)/a(n-1) = (8 + 3*sqrt(7))^2. (End)

Edited by N. J. A. Sloane at the suggestion of Richard Choulet, Sep 22 2007

A055560 Base numbers of 9-gonal palindromic numbers.

Original entry on oeis.org

1, 2, 6, 12, 17, 44, 74, 139, 1123, 1411, 2101, 4070, 11323, 11472, 12870, 16318, 16853, 18729, 52642, 132619, 435644, 446904, 168566853, 350096787, 521037077, 708609429, 1121857192, 1641773578, 11947307367, 21633254881, 75356090494

Offset: 1

J. Lowell, Jul 10 2000

P. De Geest, Palindromic nonagonals

Cf. A001106, A082723.

Select[Range[0, 10^5], PalindromeQ[PolygonalNumber[9, #]] &] (* Robert Price, Apr 29 2019 *)

9-gonal numbers are of the form (n(7n-5))/2.

Edited and extended by Patrick De Geest, Apr 13 2003.

A172076 a(n) = n(n+1)(14*n-11)/6.

Original entry on oeis.org

0, 1, 17, 62, 150, 295, 511, 812, 1212, 1725, 2365, 3146, 4082, 5187, 6475, 7960, 9656, 11577, 13737, 16150, 18830, 21791, 25047, 28612, 32500, 36725, 41301, 46242, 51562, 57275, 63395, 69936, 76912, 84337, 92225, 100590, 109446, 118807, 128687

Offset: 0

Vincenzo Librandi, Jan 25 2010

Generated by the formula n*(n+1)*(2*d*n-(2*d-3))/6 for d=7.
From Bruno Berselli, Dec 14 2010: (Start)
In fact, the sequence is related to A001106 by a(n) = n*A001106(n) - Sum_{k=0..n-1} A001106(k) and this is the case d=7 in the identity n*(n*(d*n-d+2)/2) - Sum_{k=0..n-1} k*(d*k-d+2)/2 = n*(n+1)*(2*d*n-2*d+3)/6.
Also 16-gonal (or hexadecagonal) pyramidal numbers.
Inverse binomial transform of this sequence: 0, 1, 15, 14, 0, 0 (0 continued). (End)

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93. [From Bruno Berselli, Feb 13 2014]

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian), 2008.
Index to sequences related to pyramidal numbers.
Index to sequences related to pyramidal numbers
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. similar sequences listed in A237616.

List([0..40], n-> n*(n+1)*(14*n-11)/6); # G. C. Greubel, Aug 30 2019

[n*(n+1)*(14*n-11)/6: n in [0..40]] // G. C. Greubel, Aug 30 2019

A172076:=n->n*(n+1)*(14*n-11)/6; seq(A172076(n), n=0..50); # Wesley Ivan Hurt, Feb 26 2014

LinearRecurrence[{4,-6,4,-1}, {0, 1, 17, 62}, 50] (* Vincenzo Librandi, Mar 01 2012 *)

vector(40, n, n*(n-1)*(14*n-25)/6) \\ G. C. Greubel, Aug 30 2019

[n*(n+1)*(14*n-11)/6 for n in (0..40)] # G. C. Greubel, Aug 30 2019

G.f.: x*(1+13*x)/(1-x)^4. - Bruno Berselli, Dec 15 2010
a(n) = Sum_{i=0..n} A051868(i). - Bruno Berselli, Dec 15 2010
a(n) = Sum_{i=0..n-1} (n-i)*(14*i+1), with a(0)=0. - Bruno Berselli, Feb 10 2014
E.g.f.: x*(6 + 45*x + 14*x^2)*exp(x)/6. - G. C. Greubel, Aug 30 2019

cp's OEIS Frontend

A262000 a(n) = n^2*(7*n - 5)/2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Formula

A276682 Number of divisors of the n-th 9-gonal number.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A051877 Partial sums of A051740.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A226489 a(n) = n*(15*n-11)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Magma

Mathematica

PARI

Formula

A302913 Determinant of n X n matrix whose main diagonal consists of the first n 9-gonal numbers and all other elements are 1's.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A317302 Square array T(n,k) = (n - 2)*(k - 1)*k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A033572 a(n) = (2*n+1)*(7*n+1).

Views

Author

Keywords

Comments

A262000 a(n) = n^2(7n - 5)/2.

A226489 a(n) = n(15n-11)/2.

A317302 Square array T(n,k) = (n - 2)(k - 1)k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.

A033572 a(n) = (2n+1)(7*n+1).

A172076 a(n) = n(n+1)(14*n-11)/6.