A256327 Number of partitions of 5n into exactly 4 parts.

0, 1, 9, 27, 64, 120, 206, 321, 478, 672, 920, 1215, 1575, 1991, 2484, 3042, 3689, 4410, 5231, 6136, 7153, 8262, 9495, 10830, 12300, 13881, 15609, 17457, 19464, 21600, 23906, 26351, 28978, 31752, 34720, 37845, 41175, 44671, 48384, 52272, 56389, 60690, 65231

Offset

0,3

Links

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

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

Formula

G.f.: x*(5*x^7+13*x^6+24*x^5+29*x^4+28*x^3+17*x^2+8*x+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)).

Example

For n=2 the 9 partitions of 5*2 = 10 are [1,1,1,7], [1,1,2,6], [1,1,3,5], [1,1,4,4], [1,2,2,5], [1,2,3,4], [1,3,3,3], [2,2,2,4] and [2,2,3,3].

Prog

(PARI) concat(0, vector(40, n, k=0; forpart(p=5*n, k++, , [4, 4]); k))
(PARI) concat(0, Vec(x*(5*x^7+13*x^6+24*x^5+29*x^4+28*x^3+17*x^2+8*x+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))

Crossrefs

Cf. A256328 (6n), A256329 (7n).

Sequence in context: A340119 A271990 A153237 * A011923 A029875 A335671

Adjacent sequences: A256324 A256325 A256326 * A256328 A256329 A256330

Keyword

nonn,easy

Author

Colin Barker, Mar 25 2015

Status

approved