A035631 Number of partitions of n into parts 5k+1 and 5k+2 with at least one part of each type.

0, 0, 1, 1, 2, 2, 3, 5, 6, 8, 9, 11, 15, 18, 23, 26, 31, 38, 45, 55, 62, 73, 85, 100, 118, 135, 155, 178, 205, 238, 269, 308, 347, 397, 452, 512, 578, 650, 733, 829, 929, 1045, 1164, 1307, 1461, 1635, 1822, 2026, 2254, 2511, 2787, 3098, 3422, 3796, 4196

Offset

1,5

Links

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

Formula

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

Mathematica

nmax = 55; s1 = Range[0, nmax/5]*5 + 1; s2 = Range[0, nmax/5]*5 + 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 = 55; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035371.

Cf. A035441-A035468, A035618-A035630, A035632-A035699.

Sequence in context: A236970 A060966 A135279 * A050046 A052337 A308858

Adjacent sequences: A035628 A035629 A035630 * A035632 A035633 A035634

Keyword

nonn

Author

Olivier Gérard

Status

approved