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A035672 Number of partitions of n into parts 8k and 8k+1 with at least one part of each type. 4
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 10, 11, 11, 11, 11, 11, 11, 11, 22, 25, 26, 26, 26, 26, 26, 26, 44, 51, 54, 55, 55, 55, 55, 55, 84, 98, 105, 108, 109, 109, 109, 109, 153, 178, 193, 200, 203, 204, 204, 204, 270, 313, 341, 356, 363, 366 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,17

LINKS

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

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8*k + 1)))*(-1 + 1/Product_{k>=1} (1 - x^(8*k))). - Robert Price, Aug 12 2020

MATHEMATICA

nmax = 70; s1 = Range[1, nmax/8]*8; s2 = Range[0, nmax/8]*8 + 1;

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

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)

nmax = 70; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035671, A035673-A035699.

Sequence in context: A080678 A096300 A333534 * A113472 A105682 A049109

Adjacent sequences:  A035669 A035670 A035671 * A035673 A035674 A035675

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified July 25 19:05 EDT 2021. Contains 346291 sequences. (Running on oeis4.)