A256329 Number of partitions of 7n into exactly 4 parts.

0, 3, 23, 72, 169, 321, 551, 864, 1285, 1815, 2484, 3289, 4263, 5400, 6736, 8262, 10018, 11990, 14222, 16698, 19464, 22500, 25857, 29511, 33516, 37845, 42555, 47616, 53089, 58939, 65231, 71928, 79097, 86697, 94800, 103361, 112455, 122034, 132176, 142830

Offset

0,2

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*(x^8+14*x^7+38*x^6+67*x^5+80*x^4+74*x^3+46*x^2+20*x+3) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)).

Example

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

Prog

(PARI)
concat(0, vector(40, n, k=0; forpart(p=7*n, k++, , [4, 4]); k))
(PARI)
concat(0, Vec(x*(x^8+14*x^7+38*x^6+67*x^5+80*x^4+74*x^3+46*x^2+20*x+3) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))

Crossrefs

Cf. A256327 (5n), A256328 (6n).

Sequence in context: A163210 A163211 A126335 * A196649 A363170 A357738

Adjacent sequences: A256326 A256327 A256328 * A256330 A256331 A256332

Keyword

nonn,easy

Author

Colin Barker, Mar 25 2015

Status

approved