A256540 Number of partitions of 4n into at most 6 parts.

1, 5, 20, 58, 136, 282, 532, 931, 1540, 2432, 3692, 5427, 7760, 10829, 14800, 19858, 26207, 34085, 43752, 55491, 69624, 86499, 106491, 130019, 157532, 189509, 226479, 269005, 317683, 373165, 436140, 507334, 587535, 677571, 778311, 890691, 1015691, 1154336

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,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).

Formula

G.f.: (3*x^8+5*x^7+11*x^6+11*x^5+13*x^4+10*x^3+8*x^2+2*x+1) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)).

a(n) = A001402(4n). - Alois P. Heinz, Apr 01 2015

Example

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

Prog

(PARI) concat(1, vector(40, n, k=0; forpart(p=4*n, k++, , [1, 6]); k))
(PARI) Vec((3*x^8+5*x^7+11*x^6+11*x^5+13*x^4+10*x^3+8*x^2+2*x+1) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)) + O(x^100))

Crossrefs

Cf. A001402, A238340 (4 parts), A256539 (5 parts).

Sequence in context: A270092 A272277 A272507 * A319888 A319869 A038165

Adjacent sequences: A256537 A256538 A256539 * A256541 A256542 A256543

Keyword

nonn,easy

Author

Colin Barker, Apr 01 2015

Status

approved