A035634 Number of partitions of n into parts 5k+2 and 5k+3 with at least one part of each type.

0, 0, 0, 0, 1, 0, 1, 1, 1, 3, 2, 3, 4, 4, 7, 6, 9, 10, 11, 16, 15, 20, 23, 25, 32, 34, 41, 47, 52, 63, 68, 80, 90, 101, 116, 129, 147, 166, 184, 210, 232, 262, 292, 326, 363, 405, 450, 501, 554, 617, 681, 756, 834, 924, 1015, 1125, 1235, 1363, 1498, 1647, 1809

Offset

1,10

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Robert Price)

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(5 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 3))). - Robert Price, Aug 16 2020

Mathematica

nmax = 61;  s1 = Range[0, nmax/5]*5 + 2; s2 = Range[0, nmax/5]*5 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 07 2020 *)
nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035633, A035635-A035699.

Sequence in context: A029150 A255246 A055923 * A091563 A161985 A292787

Adjacent sequences: A035631 A035632 A035633 * A035635 A035636 A035637

Keyword

nonn

Author

Olivier Gérard

Status

approved