A035638 Number of partitions of n into parts 6k and 6k+2 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 4, 0, 4, 0, 4, 0, 10, 0, 11, 0, 11, 0, 22, 0, 25, 0, 26, 0, 44, 0, 51, 0, 54, 0, 84, 0, 98, 0, 105, 0, 152, 0, 178, 0, 193, 0, 266, 0, 312, 0, 341, 0, 452, 0, 528, 0, 581, 0, 749, 0, 873, 0, 964, 0, 1214, 0, 1409, 0, 1561, 0, 1930, 0, 2234

Offset

1,14

Links

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

Formula

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - Robert Price, Aug 12 2020

Mathematica

nmax = 76; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 2;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 76; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035637, A035639-A035699.

Sequence in context: A246130 A010675 A035673 * A347156 A292142 A345450

Adjacent sequences: A035635 A035636 A035637 * A035639 A035640 A035641

Keyword

nonn

Author

Olivier Gérard

Status

approved