A035685 Number of partitions of n into parts 8k+2 and 8k+3 with at least one part of each type.

0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 4, 2, 4, 4, 5, 4, 7, 5, 10, 7, 12, 11, 14, 13, 18, 15, 24, 19, 28, 27, 33, 31, 42, 36, 51, 45, 60, 58, 71, 68, 87, 79, 103, 96, 120, 118, 141, 137, 169, 159, 197, 189, 228, 226, 266, 262, 314, 302, 362, 355, 416, 416, 482, 478, 561, 550

Offset

1,11

Links

Robert Price, Table of n, a(n) for n = 1..1000

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 3))). - Robert Price, Aug 15 2020

Mathematica

nmax = 68; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035684, A035686-A035699.

Sequence in context: A296604 A261211 A233521 * A205509 A118736 A201161

Adjacent sequences: A035682 A035683 A035684 * A035686 A035687 A035688

Keyword

nonn

Author

Olivier Gérard

Status

approved