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A035630 Number of partitions of n into parts 5k and 5k+4 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 3, 0, 0, 1, 3, 6, 0, 1, 3, 7, 11, 1, 3, 7, 14, 19, 3, 7, 15, 26, 32, 7, 15, 29, 46, 51, 15, 30, 53, 76, 81, 30, 56, 91, 124, 126, 57, 98, 152, 195, 195, 101, 167, 245, 304, 296, 174, 274, 388, 461, 448, 289, 441, 598, 696, 668, 470 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

LINKS

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

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+4)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - Robert Price, Aug 07 2020

MATHEMATICA

nmax = 70; s1 = Range[1, nmax/5]*5; 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 06 2020 *)

nmax = 70; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 06 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035629, A035631-A035699.

Sequence in context: A035696 A170840 A300725 * A126723 A325846 A325735

Adjacent sequences:  A035627 A035628 A035629 * A035631 A035632 A035633

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)