A190705 a(n) = 6*n^2*(2*n + 1).

0, 18, 120, 378, 864, 1650, 2808, 4410, 6528, 9234, 12600, 16698, 21600, 27378, 34104, 41850, 50688, 60690, 71928, 84474, 98400, 113778, 130680, 149178, 169344, 191250, 214968, 240570, 268128, 297714, 329400

Offset: 0

Author

Adi Dani, Jun 14 2011

Keywords

• nonn
• easy

Comments

Number of partitions of 12*n + 1 into 4 parts.

Examples

			a(1)=18: there are 18 partitions of 12*1+1=13 into 4 parts:
  [1,1,1,10], [1,1,2,9], [1,1,3,8], [1,1,4,7], [1,1,5,6],
  [1,2,2,8],  [1,2,3,7], [1,2,4,6], [1,2,5,5], [1,3,3,6],
  [1,3,4,5],  [1,4,4,4], [2,2,2,7], [2,2,3,6], [2,2,4,5],
  [2,3,3,5],  [2,3,4,4], [3,3,3,4].
		

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).

Programs

Magma

[6*n^2*(2*n+1): n in [0..40]]; // Vincenzo Librandi, Jun 14 2011

Mathematica

Table[6n^2(2n + 1), {n, 0, 30}]
LinearRecurrence[{4,-6,4,-1},{0,18,120,378},40] (* Harvey P. Dale, Mar 20 2016 *)

PARI

a(n)=6*n^2*(2*n+1) \\ Charles R Greathouse IV, Aug 05 2013

Formula

a(n) = 6 * A099721(n).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=18, a(2)=120, a(3)=378. - Harvey P. Dale, Mar 20 2016