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A035662 Number of partitions of n into parts 7k+2 and 7k+3 with at least one part of each type. 3
0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 3, 2, 4, 4, 4, 5, 6, 8, 7, 11, 11, 12, 14, 16, 19, 19, 25, 26, 29, 32, 37, 41, 43, 53, 56, 61, 69, 77, 83, 90, 106, 110, 123, 135, 149, 160, 176, 197, 210, 231, 253, 276, 297, 323, 359, 381, 418, 453, 494, 526, 576, 627, 669, 728, 790 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 125 terms from Robert Price)

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 3))). - Robert Price, Aug 16 2020

MATHEMATICA

nmax = 66; s1 = Range[0, nmax/7]*7 + 2; s2 = Range[0, nmax/7]*7 + 3;

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

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 14 2020 *)

nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035661, A035663-A035699.

Sequence in context: A235728 A205546 A081315 * A249870 A325404 A324750

Adjacent sequences:  A035659 A035660 A035661 * A035663 A035664 A035665

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)