A035627 Number of partitions of n into parts 5k and 5k+1 with at least one part of each type.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 10, 11, 11, 11, 11, 22, 25, 26, 26, 26, 44, 51, 54, 55, 55, 84, 98, 105, 108, 109, 153, 178, 193, 200, 203, 270, 313, 341, 356, 363, 462, 532, 582, 611, 626, 771, 883, 968, 1021, 1050, 1259, 1431, 1571, 1663, 1717, 2017

Offset

1,11

Links

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

Formula

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

Mathematica

nmax = 61; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 1;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 06 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035626, A035628-A035699.

Sequence in context: A262690 A048760 A287392 * A228423 A165923 A228729

Adjacent sequences: A035624 A035625 A035626 * A035628 A035629 A035630

Keyword

nonn

Author

Olivier Gérard

Status

approved