A396144 Number of strict integer partitions of 2*n with reverse-alternating sum -6.

0, 0, 0, 0, 1, 1, 1, 2, 3, 5, 7, 10, 13, 17, 22, 29, 37, 47, 59, 73, 89, 109, 131, 158, 188, 224, 263, 310, 361, 421, 486, 562, 644, 739, 841, 958, 1084, 1227, 1380, 1554, 1739, 1947, 2169, 2417, 2681, 2975, 3286, 3631, 3997, 4400, 4826, 5295, 5789, 6330, 6901, 7523, 8178, 8891, 9639, 10451

Offset

0,8

Comments

Also the number of partitions of n+18 into 6 distinct parts not containing the part 6.

Links

Table of n, a(n) for n=0..59.

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).

Formula

G.f.: Sum_{j=1..6} q^(j^2+3) * q_binomial(5,j-1) / Product_{k=1..j} (1-q^k).

a(n) + A395257(n) = A001402(n-3) = A026812(n+3).

a(n) = a(n-1) + a(n-2) - a(n-5) - 2*a(n-7) + a(n-9) + a(n-10) + a(n-11) + a(n-12) - 2*a(n-14) - a(n-16) + a(n-19) + a(n-20) - a(n-21) for n > 39.

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=60, q='q+O('q^N)); concat([0, 0, 0, 0], Vec(sum(j=1, 6, q^(j^2+3)*q_binomial(5, j-1)/prod(k=1, j, 1-q^k))))

Crossrefs

Column k=3 of A396143.

Cf. A001402, A026812, A275216, A395257.

Sequence in context: A177332 A318155 A385069 * A282569 A372618 A213213

Adjacent sequences: A396141 A396142 A396143 * A396145 A396146 A396147

Keyword

nonn

Author

Seiichi Manyama, May 18 2026

Status

approved