login
Number of partitions of n with six parts in which no part occurs more than twice.
2

%I #8 Dec 19 2022 14:00:15

%S 1,1,3,5,8,11,18,23,33,44,58,73,96,117,148,181,221,264,321,377,449,

%T 526,616,712,830,949,1093,1246,1420,1605,1822,2044,2302,2575,2880,

%U 3202,3569,3947,4375,4826,5322,5844,6427,7029,7698,8400,9164,9965,10846,11757

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

%H Alois P. Heinz, <a href="/A320594/b320594.txt">Table of n, a(n) for n = 12..10000</a>

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1).

%F 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).

%t 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 *)

%Y Column k=6 of A209318.

%K nonn,easy

%O 12,3

%A _Alois P. Heinz_, Oct 16 2018