A035645 Number of partitions of n into parts 6k+1 and 6k+5 with at least one part of each type.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 4, 4, 4, 4, 5, 7, 10, 11, 11, 12, 14, 18, 23, 25, 27, 29, 33, 40, 47, 53, 57, 62, 70, 81, 94, 104, 113, 123, 137, 156, 175, 194, 211, 230, 255, 285, 317, 348, 379, 413, 454, 502, 552, 604, 657, 715, 782, 857, 937, 1021, 1109, 1203

Offset

1,11

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Robert Price)

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 5))). - Robert Price, Aug 16 2020

Mathematica

nmax = 63; s1 = Range[0, nmax/6]*6 + 1; s2 = Range[0, nmax/6]*6 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)
nmax = 63; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035644, A035646-A035699.

Sequence in context: A046930 A302254 A160409 * A063440 A008497 A220497

Adjacent sequences: A035642 A035643 A035644 * A035646 A035647 A035648

Keyword

nonn

Author

Olivier Gérard

Status

approved