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A035686
Number of partitions of n into parts 8k+2 and 8k+4 with at least one part of each type.
4
0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 5, 0, 5, 0, 8, 0, 8, 0, 14, 0, 15, 0, 22, 0, 23, 0, 34, 0, 37, 0, 51, 0, 54, 0, 74, 0, 81, 0, 107, 0, 116, 0, 150, 0, 165, 0, 210, 0, 229, 0, 287, 0, 316, 0, 392, 0, 430, 0, 526, 0, 580, 0, 704, 0, 774, 0, 929, 0, 1024, 0, 1223, 0, 1347, 0
OFFSET
1,10
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 4))). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 77; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 77; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
KEYWORD
nonn
STATUS
approved