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A035699
Number of partitions of n into parts 8k+6 and 8k+7 with at least one part of each type.
82
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 3, 2, 3, 0, 1, 1, 3, 3, 6, 4, 5, 1, 3, 3, 7, 7, 11, 7, 8, 3, 7, 8, 15, 13, 19, 12, 13, 8, 16, 17, 27, 24, 30, 20, 23, 18, 32, 32, 46, 40, 48, 34, 41, 37, 56, 57, 76, 66, 76, 58, 71, 67, 97, 96, 122, 105, 119
OFFSET
1,21
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 6)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 83; s1 = Range[0, nmax/8]*8 + 6; 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 16 2020 *)
nmax = 83; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020*)
CROSSREFS
KEYWORD
nonn
STATUS
approved