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A339373
Number of partitions of n into an even number of triangular numbers.
4
1, 0, 1, 0, 2, 0, 3, 1, 3, 2, 4, 3, 6, 5, 6, 6, 10, 7, 13, 10, 15, 13, 20, 15, 26, 21, 28, 26, 36, 31, 44, 42, 49, 50, 61, 57, 75, 73, 84, 85, 103, 97, 123, 121, 137, 140, 166, 159, 194, 194, 216, 225, 256, 253, 295, 304, 330, 346, 389, 387, 446, 456, 498, 516, 579, 576
OFFSET
0,5
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(6) = 3 because we have [3, 3], [3, 1, 1, 1] and [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