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A339367
Number of partitions of n into an odd number of distinct squares.
5
0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 2, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 2, 3
OFFSET
0,50
FORMULA
G.f.: (1/2) * (Product_{k>=1} (1 + x^(k^2)) - Product_{k>=1} (1 - x^(k^2))).
a(n) = (A033461(n) - A276516(n)) / 2.
EXAMPLE
a(49) = 2 because we have [49] and [36, 9, 4].
MATHEMATICA
nmax = 90; CoefficientList[Series[(1/2) (Product[(1 + x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}] - Product[(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 01 2020
STATUS
approved