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A035631 Number of partitions of n into parts 5k+1 and 5k+2 with at least one part of each type. 3
0, 0, 1, 1, 2, 2, 3, 5, 6, 8, 9, 11, 15, 18, 23, 26, 31, 38, 45, 55, 62, 73, 85, 100, 118, 135, 155, 178, 205, 238, 269, 308, 347, 397, 452, 512, 578, 650, 733, 829, 929, 1045, 1164, 1307, 1461, 1635, 1822, 2026, 2254, 2511, 2787, 3098, 3422, 3796, 4196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(5 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 2))). - Robert Price, Aug 16 2020

MATHEMATICA

nmax = 55; s1 = Range[0, nmax/5]*5 + 1; s2 = Range[0, nmax/5]*5 + 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^(5 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020 *)

CROSSREFS

Cf. A035371.

Cf. A035441-A035468, A035618-A035630, A035632-A035699.

Sequence in context: A236970 A060966 A135279 * A050046 A052337 A308858

Adjacent sequences: A035628 A035629 A035630 * A035632 A035633 A035634

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 28 05:29 EST 2022. Contains 358407 sequences. (Running on oeis4.)