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A339376
Number of partitions of n into an odd number of distinct triangular numbers.
4
0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 1, 0, 3, 0, 1, 1, 2, 0, 1, 2, 1, 3, 0, 2, 1, 2, 1, 1, 2, 2, 3, 1, 1, 3, 2, 0, 4, 3, 2, 3, 2, 2, 2, 3, 2, 4, 2, 3, 2, 3, 4, 4, 4, 1, 5, 4, 2, 3, 5, 3, 6, 4, 2, 6, 4, 3, 5, 6, 5, 5, 5, 5, 5, 4, 5
OFFSET
0,11
FORMULA
G.f.: (1/2) * (Product_{k>=1} (1 + x^(k*(k + 1)/2)) - Product_{k>=1} (1 - x^(k*(k + 1)/2))).
a(n) = (A024940(n) - A292518(n)) / 2.
EXAMPLE
a(28) = 3 because we have [28], [21, 6, 1] and [15, 10, 3].
MATHEMATICA
nmax = 90; CoefficientList[Series[(1/2) (Product[(1 + x^(k (k + 1)/2)), {k, 1, nmax}] - Product[(1 - x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 02 2020
STATUS
approved