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A035680
Number of partitions of n into parts 8k+1 and 8k+3 with at least one part of each type.
2
0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 6, 6, 8, 9, 9, 11, 12, 15, 18, 19, 23, 26, 27, 31, 34, 39, 45, 49, 56, 62, 66, 74, 80, 89, 101, 109, 123, 136, 144, 160, 173, 187, 210, 227, 249, 275, 293, 319, 346, 371, 408, 442, 480, 525, 562, 608, 655, 701, 763, 822, 887, 963
OFFSET
1,7
FORMULA
G.f. : (-1 + 1/Product_{k>=0} (1 - x^(8 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 3). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 64; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 64; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
CROSSREFS
Sequence in context: A240869 A367395 A065308 * A238220 A103600 A267160
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified September 20 10:44 EDT 2024. Contains 376068 sequences. (Running on oeis4.)