A035636 Number of partitions of n into parts 5k+3 and 5k+4 with at least one part of each type.

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 3, 3, 4, 3, 4, 7, 7, 8, 8, 10, 14, 14, 16, 18, 20, 27, 28, 30, 35, 40, 48, 52, 55, 64, 73, 85, 90, 98, 114, 128, 143, 155, 168, 195, 214, 237, 259, 283, 319, 353, 385, 422, 460, 516, 564, 618, 672, 734, 816, 892, 964, 1057

Offset

1,12

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(5 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 4))). - Robert Price, Aug 16 2020

Mathematica

nmax = 66;  s1 = Range[0, nmax/5]*5 + 3; s2 = Range[0, nmax/5]*5 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 07 2020 *)
nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035635, A035637-A035699.

Sequence in context: A301502 A260056 A269699 * A104554 A372893 A293304

Adjacent sequences: A035633 A035634 A035635 * A035637 A035638 A035639

Keyword

nonn

Author

Olivier Gérard

Status

approved