A256314 Number of partitions of 3n into exactly 5 parts.

0, 0, 1, 5, 13, 30, 57, 101, 164, 255, 377, 540, 748, 1014, 1342, 1747, 2233, 2818, 3507, 4319, 5260, 6351, 7599, 9027, 10642, 12470, 14518, 16814, 19366, 22204, 25337, 28796, 32591, 36756, 41301, 46262, 51649, 57501, 63829, 70673, 78045, 85987, 94512

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,-1,-2,2,1,-2,2,0,-2,1).

Formula

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

Example

For n=3 the 5 partitions of 3*3 = 9 are [1,1,1,1,5], [1,1,1,2,4], [1,1,1,3,3], [1,1,2,2,3] and [1,2,2,2,2].

Mathematica

Table[Length[IntegerPartitions[3n, {5}]], {n, 0, 50}] (* Harvey P. Dale, Jul 21 2019 *)

Prog

(PARI) concat(0, vector(40, n, k=0; forpart(p=3*n, k++, , [5, 5]); k))
(PARI) concat([0, 0], Vec(-x^2*(2*x^7+3*x^6+4*x^5+5*x^4+6*x^3+3*x^2+3*x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^4+x^3+x^2+x+1)) + O(x^100)))

Crossrefs

Cf. A077043, A256313, A256315.

Sequence in context: A182069 A085555 A224888 * A002768 A354292 A086522

Adjacent sequences: A256311 A256312 A256313 * A256315 A256316 A256317

Keyword

nonn,easy

Author

Colin Barker, Mar 23 2015

Status

approved