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A035788
Number of partitions of n into parts 6k+4 and 6k+5 with at least one part of each type.
1
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 0, 1, 1, 3, 2, 4, 1, 3, 3, 7, 5, 7, 3, 8, 8, 13, 9, 13, 9, 17, 15, 24, 18, 24, 19, 32, 30, 41, 32, 44, 38, 57, 52, 70, 59, 75, 69, 98, 92, 116, 99, 128, 122, 163, 152, 187, 169, 211, 205, 264, 249, 298, 275, 342, 338, 416, 395, 468
OFFSET
1,15
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 5))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 73; s1 = Range[0, nmax/6]*6 + 4; s2 = Range[0, nmax/6]*6 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 16 2020 *)
nmax = 73; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020*)
CROSSREFS
KEYWORD
nonn
STATUS
approved