A395257 Number of strict integer partitions of 2*n with reverse-alternating sum 6.

0, 0, 0, 1, 0, 1, 2, 3, 4, 6, 7, 10, 13, 18, 22, 29, 34, 43, 51, 63, 74, 90, 104, 124, 143, 167, 191, 222, 251, 288, 325, 369, 413, 467, 519, 582, 645, 718, 792, 878, 963, 1062, 1162, 1275, 1389, 1519, 1649, 1796, 1945, 2110, 2278, 2465, 2653, 2862, 3074, 3306, 3542, 3801, 4063

Offset

0,7

Comments

Also the number of partitions of n+18 into 6 distinct parts containing the part 6.

Links

Table of n, a(n) for n=0..58.

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,-1,-1,1,1,1,0,0,-1,-1,1).

Formula

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

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

a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-6) - a(n-7) + a(n-8) + a(n-9) + a(n-10) - a(n-13) - a(n-14) + a(n-15) for n > 33.

Prog

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

Crossrefs

Column k=3 of A344649.

Cf. A395222.

Sequence in context: A199118 A035941 A039854 * A237752 A032480 A226137

Adjacent sequences: A395254 A395255 A395256 * A395258 A395259 A395260

Keyword

nonn

Author

Seiichi Manyama, May 16 2026

Status

approved