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A035640
Number of partitions of n into parts 6k and 6k+4 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 3, 0, 7, 0, 3, 0, 8, 0, 14, 0, 8, 0, 17, 0, 26, 0, 18, 0, 33, 0, 47, 0, 36, 0, 61, 0, 81, 0, 68, 0, 106, 0, 137, 0, 121, 0, 181, 0, 224, 0, 209, 0, 296, 0, 362, 0, 347, 0, 478, 0, 570, 0, 565, 0, 750, 0, 890, 0, 894, 0, 1166, 0
OFFSET
1,16
LINKS
FORMULA
G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 4)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - Robert Price, Aug 12 2020
MATHEMATICA
nmax = 81; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 81; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 12 2020 *)
CROSSREFS
Bisections give: A035619 (even part), A000004 (odd part).
Sequence in context: A213543 A374204 A247254 * A079327 A340504 A242447
KEYWORD
nonn
STATUS
approved