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A339366 Number of partitions of n into an even number of distinct squares. 5
1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 3, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 3, 1, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,51

LINKS

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

Index entries for sequences related to partitions

Index entries for sequences related to sums of squares

FORMULA

G.f.: (1/2) * (Product_{k>=1} (1 + x^(k^2)) + Product_{k>=1} (1 - x^(k^2))).

a(n) = (A033461(n) + A276516(n)) / 2.

EXAMPLE

a(50) = 2 because we have [49, 1] and [36, 9, 4, 1].

MATHEMATICA

nmax = 90; CoefficientList[Series[(1/2) (Product[(1 + x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}] + Product[(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A000290, A033461, A067661, A276516, A339364, A339365, A339367.

Sequence in context: A321759 A076882 A229745 * A016397 A238450 A251926

Adjacent sequences:  A339363 A339364 A339365 * A339367 A339368 A339369

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 01 2020

STATUS

approved

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Last modified September 27 17:05 EDT 2021. Contains 347693 sequences. (Running on oeis4.)