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A339374
Number of partitions of n into an odd number of triangular numbers.
4
0, 1, 0, 2, 0, 2, 1, 3, 1, 4, 3, 4, 4, 6, 5, 9, 7, 10, 9, 14, 10, 19, 15, 21, 18, 27, 22, 34, 30, 37, 37, 47, 43, 57, 56, 64, 66, 80, 75, 96, 94, 108, 110, 131, 125, 155, 154, 173, 178, 207, 201, 240, 245, 267, 280, 315, 315, 364, 374, 406, 423, 477, 473, 543, 555, 604
OFFSET
0,4
FORMULA
G.f.: (1/2) * (Product_{k>=1} 1 / (1 - x^(k*(k + 1)/2)) - Product_{k>=1} 1 / (1 + x^(k*(k + 1)/2))).
a(n) = (A007294(n) - A292519(n)) / 2.
EXAMPLE
a(7) = 3 because we have [3, 3, 1], [3, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 65; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k (k + 1)/2)), {k, 1, nmax}] - Product[1/(1 + x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 02 2020
STATUS
approved