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A035619 Number of partitions of n into parts 3k and 3k+2 with at least one part of each type. 4
0, 0, 0, 0, 1, 0, 1, 3, 1, 3, 7, 3, 8, 14, 8, 17, 26, 18, 33, 47, 36, 61, 81, 68, 106, 137, 121, 181, 224, 209, 296, 362, 347, 478, 570, 565, 750, 890, 894, 1166, 1360, 1396, 1774, 2062, 2134, 2677, 3076, 3228, 3973, 4555, 4804, 5854, 6657, 7085, 8513 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 80 terms from Robert Price)

FORMULA

G.f.: (-1 + 1/Product_{k>=1} (1 - x^(3 k)))*(-1 + 1/Product_{k>=0} (1 - x^(3 k + 2))). - Robert Price, Aug 16 2020

MATHEMATICA

nmax = 55; s1 = Range[1, nmax/3]*3; s2 = Range[0, nmax/3]*3 + 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^(3 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(3 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020*)

CROSSREFS

Cf. A035441-A035468, A035618, A035620-A035699.

Sequence in context: A209766 A114972 A107461 * A280995 A092689 A281553

Adjacent sequences:  A035616 A035617 A035618 * A035620 A035621 A035622

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified September 24 15:39 EDT 2021. Contains 347643 sequences. (Running on oeis4.)