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A035684
Number of partitions of n into parts 8k+1 and 8k+7 with at least one part of each type.
4
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 4, 4, 4, 4, 4, 4, 5, 7, 10, 11, 11, 11, 11, 12, 14, 18, 23, 25, 26, 26, 27, 29, 33, 40, 47, 52, 54, 56, 58, 62, 70, 81, 93, 101, 107, 111, 116, 124, 137, 155, 172, 188, 199, 208, 218, 233, 255, 282, 311, 336, 357, 374, 393
OFFSET
1,15
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 68; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 7;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
KEYWORD
nonn
STATUS
approved