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A035695
Number of partitions of n into parts 8k+4 and 8k+6 with at least one part of each type.
4
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 3, 0, 1, 0, 4, 0, 3, 0, 7, 0, 4, 0, 10, 0, 8, 0, 15, 0, 11, 0, 21, 0, 18, 0, 30, 0, 24, 0, 42, 0, 37, 0, 56, 0, 50, 0, 78, 0, 70, 0, 102, 0, 95, 0, 137, 0, 129, 0, 179, 0, 171, 0, 236, 0, 227, 0, 303, 0, 297, 0, 395, 0, 386, 0, 502, 0
OFFSET
1,18
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 83; s1 = Range[0, nmax/8]*8 + 4; 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 16 2020 *)
nmax = 83; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020*)
CROSSREFS
Bisections give A035626 (even part), A000004 (odd part).
Sequence in context: A111526 A117178 A111527 * A100257 A318315 A373951
KEYWORD
nonn
STATUS
approved