A035788 Number of partitions of n into parts 6k+4 and 6k+5 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 0, 1, 1, 3, 2, 4, 1, 3, 3, 7, 5, 7, 3, 8, 8, 13, 9, 13, 9, 17, 15, 24, 18, 24, 19, 32, 30, 41, 32, 44, 38, 57, 52, 70, 59, 75, 69, 98, 92, 116, 99, 128, 122, 163, 152, 187, 169, 211, 205, 264, 249, 298, 275, 342, 338, 416, 395, 468

Offset

1,15

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 5))). - Robert Price, Aug 16 2020

Mathematica

nmax = 73; s1 = Range[0, nmax/6]*6 + 4; 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 16 2020 *)
nmax = 73; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 4)), {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-A035699.

Sequence in context: A107261 A265336 A219782 * A097559 A293108 A172237

Adjacent sequences: A035785 A035786 A035787 * A035789 A035790 A035791

Keyword

nonn

Author

Olivier Gérard

Status

approved