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A339375
Number of partitions of n into an even number of distinct triangular numbers.
4
1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 0, 3, 1, 0, 2, 1, 1, 1, 3, 1, 2, 0, 2, 2, 0, 2, 3, 3, 1, 2, 2, 2, 2, 2, 1, 4, 4, 1, 3, 2, 3, 2, 3, 1, 5, 4, 2, 4, 2, 4, 4, 3, 2, 6, 4, 3, 4, 5, 2, 3, 6, 5, 6, 5, 4, 5, 5, 4, 5, 6, 4
OFFSET
0,17
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(31) = 3 because we have [28, 3], [21, 10] and [21, 6, 3, 1].
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