A191745 a(n) = 12*n^3 + 9*n^2 + 2*n.

0, 23, 136, 411, 920, 1735, 2928, 4571, 6736, 9495, 12920, 17083, 22056, 27911, 34720, 42555, 51488, 61591, 72936, 85595, 99640, 115143, 132176, 150811, 171120, 193175, 217048, 242811, 270536, 300295, 332160

Offset

0,2

Comments

Number of partitions of 12*n+2 into 4 parts.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Example

a(1)=23: there are 23 partitions of 12*1+2=14 into 4 parts: [1,1,1,11], [1,1,2,10], [1,1,3,9], [1,1,4,8], [1,1,5,7], [1,1,6,6], [1,2,2,9], [1,2,3,8], [1,2,4,7], [1,2,5,6], [1,3,3,7], [1,3,4,6], [1,3,5,5], [1,4,4,5], [2,2,2,8], [2,2,3,7], [2,2,4,6], [2,2,5,5], [2,3,3,6], [2,3,4,5], [2,4,4,4], [3,3,3,5], [3,3,4,4].

Mathematica

Table[12n^3 + 9n^2 + 2n, {n, 0, 30}]
LinearRecurrence[{4, -6, 4, -1}, {0, 23, 136, 411}, 40] (* Harvey P. Dale, Nov 05 2019 *)

Prog

(Magma) [12*n^3+9*n^2+2*n: n in [0..40]]; // Vincenzo Librandi, Jun 14 2011
(PARI) a(n)=((12*n+9)*n+2)*n /* Charles R Greathouse IV, Jun 14 2011 */

Crossrefs

Sequence in context: A157907 A039613 A009482 * A260842 A093806 A142679

Adjacent sequences: A191742 A191743 A191744 * A191746 A191747 A191748

Keyword

nonn,easy

Author

Adi Dani, Jun 14 2011

Status

approved