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A035688
Number of partitions of n into parts 8k+2 and 8k+6 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 4, 0, 4, 0, 5, 0, 7, 0, 10, 0, 12, 0, 14, 0, 18, 0, 24, 0, 28, 0, 33, 0, 41, 0, 50, 0, 59, 0, 70, 0, 84, 0, 100, 0, 117, 0, 137, 0, 161, 0, 188, 0, 219, 0, 254, 0, 295, 0, 341, 0, 393, 0, 453, 0, 520, 0, 595, 0, 682, 0, 780, 0, 889, 0
OFFSET
1,14
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 79; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 6;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 79; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
KEYWORD
nonn
STATUS
approved