OFFSET
0,9
COMMENTS
Also the number of partitions of n+32 into 8 distinct parts not containing the part 8.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, 0, -1, 0, -1, 0, 1, 2, 1, 0, 1, -1, -1, -2, -1, -1, 1, 0, 1, 2, 1, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, -1).
FORMULA
G.f.: Sum_{j=1..8} q^(j^2+4) * q_binomial(7,j-1) / Product_{k=1..j} (1-q^k).
a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-9) + a(n-11) + 2*a(n-12) + a(n-13) + a(n-15) - a(n-16) - a(n-17) - 2*a(n-18) - a(n-19) - a(n-20) + a(n-21) + a(n-23) + 2*a(n-24) + a(n-25) - a(n-27) - a(n-29) - a(n-31) + a(n-34) + a(n-35) - a(n-36) for n > 68.
PROG
(PARI) q_binomial(n, k) = if(k<0 || k>n, 0, prod(j=1, k, 1-q^(n-j+1))/prod(j=1, k, 1-q^j));
my(N=70, q='q+O('q^N)); concat([0, 0, 0, 0, 0], Vec(sum(j=1, 8, q^(j^2+4)*q_binomial(7, j-1)/prod(k=1, j, 1-q^k))))
CROSSREFS
KEYWORD
nonn,new
AUTHOR
Seiichi Manyama, May 18 2026
STATUS
approved
