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A339376 Number of partitions of n into an odd number of distinct triangular numbers. 4
0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 1, 0, 3, 0, 1, 1, 2, 0, 1, 2, 1, 3, 0, 2, 1, 2, 1, 1, 2, 2, 3, 1, 1, 3, 2, 0, 4, 3, 2, 3, 2, 2, 2, 3, 2, 4, 2, 3, 2, 3, 4, 4, 4, 1, 5, 4, 2, 3, 5, 3, 6, 4, 2, 6, 4, 3, 5, 6, 5, 5, 5, 5, 5, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

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(28) = 3 because we have [28], [21, 6, 1] and [15, 10, 3].

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, A067659, A292518, A339367, A339373, A339374, A339375.

Sequence in context: A220400 A285108 A030216 * A159459 A304095 A276675

Adjacent sequences:  A339373 A339374 A339375 * A339377 A339378 A339379

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 02 2020

STATUS

approved

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Last modified September 27 19:23 EDT 2021. Contains 347694 sequences. (Running on oeis4.)