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A035639
Number of partitions of n into parts 6k and 6k+3 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 4, 0, 0, 4, 0, 0, 10, 0, 0, 11, 0, 0, 22, 0, 0, 25, 0, 0, 44, 0, 0, 51, 0, 0, 83, 0, 0, 98, 0, 0, 149, 0, 0, 177, 0, 0, 259, 0, 0, 309, 0, 0, 436, 0, 0, 521, 0, 0, 716, 0, 0, 857, 0, 0, 1151, 0, 0, 1376, 0, 0, 1816, 0, 0, 2170, 0, 0, 2818, 0, 0
OFFSET
1,15
LINKS
FORMULA
G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 3)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - Robert Price, Aug 12 2020
MATHEMATICA
nmax = 83; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 83; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 12 2020 *)
CROSSREFS
First trisection gives A006477.
Sequence in context: A308277 A278216 A036480 * A284689 A037214 A245198
KEYWORD
nonn
STATUS
approved