A035633 Number of partitions of n into parts 5k+1 and 5k+4 with at least one part of each type.

0, 0, 0, 0, 1, 1, 1, 1, 2, 4, 4, 4, 5, 7, 10, 11, 12, 14, 18, 23, 26, 29, 33, 40, 48, 55, 61, 70, 82, 96, 108, 121, 137, 158, 179, 202, 226, 255, 288, 325, 363, 406, 453, 508, 566, 632, 701, 781, 867, 963, 1066, 1182, 1306, 1445, 1592, 1759, 1939, 2139, 2350

Offset

1,9

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 100 terms from Robert Price)

Formula

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

Mathematica

nmax = 59; s1 = Range[0, nmax/5]*5 + 1; 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 = 59; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 1)), {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-A035632, A035634-A035699.

Sequence in context: A227190 A284581 A284560 * A160803 A278481 A084291

Adjacent sequences: A035630 A035631 A035632 * A035634 A035635 A035636

Keyword

nonn

Author

Olivier Gérard

Status

approved