A256225 Number of partitions of 5n into 5 parts.

0, 1, 7, 30, 84, 192, 377, 674, 1115, 1747, 2611, 3765, 5260, 7166, 9542, 12470, 16019, 20282, 25337, 31289, 38225, 46262, 55496, 66055, 78045, 91606, 106852, 123935, 142979, 164147, 187572, 213429, 241860, 273052, 307156, 344370, 384855, 428821, 476437, 527925

Offset: 0

Author

Colin Barker, Mar 19 2015

Keywords

• nonn
• easy

Examples

			For n=2, the 7 partitions of 10 are [6,1,1,1,1], [5,2,1,1,1], [4,3,1,1,1], [4,2,2,1,1], [3,3,2,1,1], [3,2,2,2,1] and [2,2,2,2,2].
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1,0,-2,2,0,1,0,-2,1).

Crossrefs

Cf. A001401, A077043, A238340, A256226, A256235.

Programs

Mathematica

Length /@ (Length /@ IntegerPartitions[5 #, {5}] & /@ Range@ 39) (* Michael De Vlieger, Mar 20 2015 *)

PARI

concat(0, Vec(-x* (x^8+5*x^7+16*x^6+25*x^5+31*x^4+25*x^3+16*x^2+5*x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))

PARI

concat(0, vector(40, n, k=0; forpart(p=5*n, k++, , [5,5]); k)) \\ Colin Barker, Mar 21 2015

Formula

G.f.: -x*(x^8+5*x^7+16*x^6+25*x^5+31*x^4+25*x^3+16*x^2+5*x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^2+x+1)).