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

0,17

LINKS

Table of n, a(n) for n=0..90.

Index entries for sequences related to partitions

Index to sequences related to polygonal numbers

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]

CROSSREFS

Cf. A000217, A024940, A067661, A292518, A339366, A339373, A339374, A339376.

Sequence in context: A317748 A090465 A052344 * A147768 A167746 A050370

Adjacent sequences:  A339372 A339373 A339374 * A339376 A339377 A339378

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 02 2020

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)