A035630 Number of partitions of n into parts 5k and 5k+4 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 3, 0, 0, 1, 3, 6, 0, 1, 3, 7, 11, 1, 3, 7, 14, 19, 3, 7, 15, 26, 32, 7, 15, 29, 46, 51, 15, 30, 53, 76, 81, 30, 56, 91, 124, 126, 57, 98, 152, 195, 195, 101, 167, 245, 304, 296, 174, 274, 388, 461, 448, 289, 441, 598, 696, 668, 470

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^(5k+4)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - Robert Price, Aug 07 2020

Mathematica

nmax = 70; s1 = Range[1, nmax/5]*5; 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 06 2020 *)
nmax = 70; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 06 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035629, A035631-A035699.

Sequence in context: A035696 A170840 A300725 * A126723 A325846 A325735

Adjacent sequences: A035627 A035628 A035629 * A035631 A035632 A035633

Keyword

nonn

Author

Olivier Gérard

Status

approved