A155156 -id:A155156 - cp's OEIS frontend

A163832 a(n) = n(2n^2 + 5*n + 1).

0, 8, 38, 102, 212, 380, 618, 938, 1352, 1872, 2510, 3278, 4188, 5252, 6482, 7890, 9488, 11288, 13302, 15542, 18020, 20748, 23738, 27002, 30552, 34400, 38558, 43038, 47852, 53012, 58530, 64418, 70688, 77352, 84422, 91910, 99828, 108188, 117002

Offset: 0

Vincenzo Librandi, Aug 05 2009

Row sums of triangle A155156.

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. A155156.

Table[n(2n^2+5n+1),{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,8,38,102},40] (* Harvey P. Dale, Feb 02 2012 *)

for(n=0, 40, print1(n*(2*n^2+5*n+1)", ")); \\ Vincenzo Librandi, Feb 22 2012

G.f.: -2*x*(1+x)*(x-4)/(x-1)^4.
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).
a(n) = A163683(n) + n = A163815(n) - 2*n = 2*A162254(n).
a(n) = -n*A168244(n+2). - Bruno Berselli, Feb 02 2012
E.g.f.: x*(8 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 05 2017

Edited by R. J. Mathar, Aug 05 2009

A163676 Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.

Original entry on oeis.org

7, 13, 23, 19, 33, 47, 25, 43, 61, 79, 31, 53, 75, 97, 119, 37, 63, 89, 115, 141, 167, 43, 73, 103, 133, 163, 193, 223, 49, 83, 117, 151, 185, 219, 253, 287, 55, 93, 131, 169, 207, 245, 283, 321, 359, 61, 103, 145, 187, 229, 271, 313, 355, 397, 439, 67, 113, 159

Offset: 1

Vincenzo Librandi, Aug 03 2009

2 + T(n,m) = (2*n+1)*(2*m+1) are composite numbers. - clarified by R. J. Mathar, Oct 16 2009

First column: A016921, second column: A017305, third column: A126980. - Vincenzo Librandi, Nov 21 2012

			Triangle begins:
   7;
  13,  23;
  19,  33,  47;
  25,  43,  61,  79;
  31,  53,  75,  97, 119;
  37,  63,  89, 115, 141, 167;
  43,  73, 103, 133, 163, 193, 223;
  49,  83, 117, 151, 185, 219, 253, 287;
  55,  93, 131, 169, 207, 245, 283, 321, 359;
  61, 103, 145, 187, 229, 271, 313, 355, 397, 439;

Vincenzo Librandi, Rows n = 1..100, flattened

Cf. A016921, A017305, A126980, A155151, A155156.

[4*n*k + 2*n + 2*k - 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012

t[n_,k_]:=4 n*k + 2n + 2k - 1; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)

for(n=1,10, for(k=1,n, print1(4*n*k + 2*n + 2*k - 1, ", "))) \\ G. C. Greubel, Aug 02 2017

T(n,m) = A155151(n,m) - 3 = A155156(n,m) - 1. - R. J. Mathar, Oct 16 2009

cp's OEIS Frontend

A163832 a(n) = n(2n^2 + 5*n + 1).

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A163676 Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.

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cp's OEIS Frontend

A163832 a(n) = n*(2*n^2 + 5*n + 1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A163676 Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A163832 a(n) = n(2n^2 + 5*n + 1).