A256524 Number of partitions of 3n into at most 4 parts.

1, 3, 9, 18, 34, 54, 84, 120, 169, 225, 297, 378, 478, 588, 720, 864, 1033, 1215, 1425, 1650, 1906, 2178, 2484, 2808, 3169, 3549, 3969, 4410, 4894, 5400, 5952, 6528, 7153, 7803, 8505, 9234, 10018, 10830, 11700, 12600, 13561, 14553, 15609, 16698, 17854, 19044

Offset

0,2

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,-2,0,2,-1).

Formula

G.f.: (x^2+x+1)*(2*x^2+1) / ((x-1)^4*(x+1)^2*(x^2+1)).

a(n) = A001400(3n). - Alois P. Heinz, Apr 01 2015

Example

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

Mathematica

LinearRecurrence[{2, 0, -2, 2, -2, 0, 2, -1}, {1, 3, 9, 18, 34, 54, 84, 120}, 50] (* Jean-François Alcover, Apr 26 2017 *)

Prog

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

Crossrefs

Cf. A001400, A077043 (3 parts), A256525 (5 parts), A256315 (6 parts).

Sequence in context: A127759 A064843 A093446 * A210970 A293406 A295862

Adjacent sequences: A256521 A256522 A256523 * A256525 A256526 A256527

Keyword

nonn,easy

Author

Colin Barker, Apr 01 2015

Status

approved