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

0,4

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(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]

CROSSREFS

Cf. A000217, A007294, A027193, A292519, A339365, A339373, A339375, A339376.

Sequence in context: A304034 A029183 A213423 * A265753 A138110 A080233

Adjacent sequences:  A339371 A339372 A339373 * A339375 A339376 A339377

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 02 2020

STATUS

approved

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Last modified August 1 17:38 EDT 2021. Contains 346402 sequences. (Running on oeis4.)