A191593 Number of partitions of 12*n into parts < 5.

1, 34, 169, 478, 1033, 1906, 3169, 4894, 7153, 10018, 13561, 17854, 22969, 28978, 35953, 43966, 53089, 63394, 74953, 87838, 102121, 117874, 135169, 154078, 174673, 197026, 221209, 247294, 275353, 305458, 337681

Offset: 0

Author

Adi Dani, Jun 07 2011

Keywords

• nonn
• easy

Comments

Number of ways of placing of 12*n indistinguishable objects into indistinguishable boxes with condition that in each box can be at most 4 objects.

Examples

			a(1)=34 all partitions of 1*12=12 into parts < 5 are:
[1,1,1,1,1,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,1,1,3],
[1,1,1,1,1,1,1,1,2,2],
[1,1,1,1,1,1,1,1,4],
[1,1,1,1,1,1,1,2,3],
[1,1,1,1,1,1,2,2,2],
[1,1,1,1,1,1,2,4],
[1,1,1,1,1,1,3,3],
[1,1,1,1,1,2,2,3],
[1,1,1,1,2,2,2,2],
[1,1,1,1,1,3,4],
[1,1,1,1,2,2,4],
[1,1,1,1,2,3,3],
[1,1,1,2,2,2,3],
[1,1,2,2,2,2,2],
[1,1,1,1,4,4],
[1,1,1,2,3,4],
[1,1,1,3,3,3],
[1,1,2,2,2,4],
[1,1,2,2,3,3],
[1,2,2,2,2,3],
[2,2,2,2,2,2],
[1,1,2,4,4],
[1,1,3,3,4],
[1,2,2,3,4],
[1,2,3,3,3],
[2,2,2,2,4],
[2,2,2,3,3],
[1,3,4,4],
[2,2,4,4],
[2,3,3,4],
[3,3,3,3],
[4,4,4].
		

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

[12*n^3+15*n^2+6*n+1: n in [0..30]]; // Vincenzo Librandi, Jun 16 2011

Mathematica

Table[12n^3 + 15n^2 + 6n + 1, {n, 0, 30}]

Formula

a(n) = 12*n^3 + 15*n^2 + 6*n + 1.

From R. J. Mathar, Jun 08 2011: (Start)

a(n) = A001400(12n) = A014126(6n).

G.f.: (1 + 30*x + 39*x^2 + 2*x^3) / (x-1)^4. (End)