A256539 Number of partitions of 4n into at most 5 parts.

1, 5, 18, 47, 101, 192, 333, 540, 831, 1226, 1747, 2418, 3266, 4319, 5608, 7166, 9027, 11229, 13811, 16814, 20282, 24260, 28796, 33940, 39744, 46262, 53550, 61667, 70673, 80631, 91606, 103664, 116875, 131310, 147042, 164147, 182702, 202787, 224484, 247877

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,4,-4,3,-2,3,-3,1).

Formula

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

a(n) = A001401(4n). - Alois P. Heinz, Apr 01 2015

Example

For n=2 the 18 partitions of 2*4 = 8 are [8], [1,7], [2,6], [3,5], [4,4], [1,1,6], [1,2,5], [1,3,4], [2,2,4], [2,3,3], [1,1,1,5], [1,1,2,4], [1,1,3,3], [1,2,2,3], [2,2,2,2], [1,1,1,1,4], [1,1,1,2,3] and [1,1,2,2,2].

Prog

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

Crossrefs

Cf. A001401, A238340 (4 parts), A256540 (6 parts).

Sequence in context: A272792 A273566 A217866 * A109363 A218214 A146213

Adjacent sequences: A256536 A256537 A256538 * A256540 A256541 A256542

Keyword

nonn,easy

Author

Colin Barker, Apr 01 2015

Status

approved