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A035629 Number of partitions of n into parts 5k and 5k+3 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 3, 1, 0, 3, 1, 6, 3, 1, 7, 3, 12, 7, 3, 15, 7, 21, 16, 7, 28, 16, 36, 31, 16, 50, 32, 60, 57, 32, 85, 60, 98, 100, 61, 141, 107, 157, 169, 110, 226, 184, 249, 276, 191, 358, 305, 388, 442, 320, 554, 495, 598, 691, 524, 848, 782, 911 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

LINKS

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

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+3)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - Robert Price, Aug 06 2020

MATHEMATICA

nmax = 68; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 3;

Table[Count[IntegerPartitions[n, All, s1~Join~s2],

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)

nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 06 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035628, A035630-A035699.

Sequence in context: A133704 A160019 A265605 * A099546 A036870 A036874

Adjacent sequences:  A035626 A035627 A035628 * A035630 A035631 A035632

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified June 24 12:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)