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A294623
Number of partitions of n into distinct generalized heptagonal numbers (A085787).
2
1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 0, 2, 3, 1, 0, 3, 3, 1, 2, 2, 1, 1, 3, 3, 3, 2, 1, 2, 3, 4, 3, 2, 2, 3, 3, 3, 5, 3, 1, 3, 4, 3, 4, 5, 2, 3, 5, 4, 3, 4, 5, 4, 4, 3, 5, 5, 3, 5, 7, 5, 3, 6, 6, 6, 6, 5, 5, 6, 6, 5, 8, 7, 5, 5, 6, 7, 8, 8
OFFSET
0,19
FORMULA
G.f.: Product_{k>=1} (1 + x^(k*(5*k-3)/2))*(1 + x^(k*(5*k+3)/2)).
EXAMPLE
a(18) = 2 because we have [18] and [13, 4, 1].
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1 + x^(k (5 k - 3)/2)) (1 + x^(k (5 k + 3)/2)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 05 2017
STATUS
approved