A035620 Number of partitions of n into parts 3k+1 and 3k+2 with at least one part of each type.

0, 0, 1, 1, 2, 4, 5, 7, 11, 14, 19, 26, 33, 43, 55, 70, 88, 111, 137, 170, 208, 256, 311, 378, 456, 551, 658, 790, 940, 1119, 1325, 1570, 1847, 2179, 2554, 2996, 3499, 4088, 4753, 5533, 6414, 7436, 8593, 9931, 11439, 13180, 15140, 17391, 19926, 22827

Offset

1,5

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 80 terms from Robert Price)

Formula

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

Mathematica

nmax = 50; s1 = Range[0, nmax/3]*3 + 1; s2 = Range[0, nmax/3]*3 + 2;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 50; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(3 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(3 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035619, A035621-A035699.

Sequence in context: A090614 A171022 A097697 * A363045 A022439 A050134

Adjacent sequences: A035617 A035618 A035619 * A035621 A035622 A035623

Keyword

nonn

Author

Olivier Gérard

Status

approved