A035662 Number of partitions of n into parts 7k+2 and 7k+3 with at least one part of each type.

0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 3, 2, 4, 4, 4, 5, 6, 8, 7, 11, 11, 12, 14, 16, 19, 19, 25, 26, 29, 32, 37, 41, 43, 53, 56, 61, 69, 77, 83, 90, 106, 110, 123, 135, 149, 160, 176, 197, 210, 231, 253, 276, 297, 323, 359, 381, 418, 453, 494, 526, 576, 627, 669, 728, 790

Offset

1,11

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 125 terms from Robert Price)

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 3))). - Robert Price, Aug 16 2020

Mathematica

nmax = 66; s1 = Range[0, nmax/7]*7 + 2; s2 = Range[0, nmax/7]*7 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 14 2020 *)
nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035661, A035663-A035699.

Sequence in context: A205546 A322348 A081315 * A249870 A325404 A324750

Adjacent sequences: A035659 A035660 A035661 * A035663 A035664 A035665

Keyword

nonn

Author

Olivier Gérard

Status

approved