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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

Index entries for sequences related to partitions

Index to sequences related to polygonal numbers

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]

CROSSREFS

Cf. A000217, A007294, A027187, A292519, A339364, A339374, A339375, A339376.

Sequence in context: A162201 A271722 A029219 * A212217 A211857 A292803

Adjacent sequences:  A339370 A339371 A339372 * A339374 A339375 A339376

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 02 2020

STATUS

approved

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Last modified July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)