A320594 Number of partitions of n with six parts in which no part occurs more than twice.

1, 1, 3, 5, 8, 11, 18, 23, 33, 44, 58, 73, 96, 117, 148, 181, 221, 264, 321, 377, 449, 526, 616, 712, 830, 949, 1093, 1246, 1420, 1605, 1822, 2044, 2302, 2575, 2880, 3202, 3569, 3947, 4375, 4826, 5322, 5844, 6427, 7029, 7698, 8400, 9164, 9965, 10846, 11757

Offset: 12

Author

Alois P. Heinz, Oct 16 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 12..10000
• Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1).

Crossrefs

Column k=6 of A209318.

Programs

Mathematica

LinearRecurrence[{1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1},{1,1,3,5,8,11,18,23,33,44,58,73,96,117,148,181,221,264,321,377,449},50] (* Harvey P. Dale, Dec 19 2022 *)

Formula

G.f.: (x^9-x^8-x^7-x^5+x^3+x^2+1)*x^12 / ((x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) *(x^2+x+1)^2 *(x+1)^3 *(x-1)^6).