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A339365 Number of partitions of n into an odd number of squares. 6
0, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 3, 2, 3, 3, 3, 4, 5, 4, 6, 5, 7, 7, 7, 8, 10, 9, 12, 10, 14, 13, 14, 15, 18, 17, 21, 20, 24, 24, 25, 27, 31, 30, 35, 34, 40, 40, 42, 45, 50, 50, 56, 55, 64, 65, 68, 72, 78, 79, 88, 85, 99, 99, 105, 110, 118, 122, 131, 132, 146, 149 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

Table of n, a(n) for n=0..70.

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

a(n) = (A001156(n) - A292520(n)) / 2.

EXAMPLE

a(9) = 3 because we have [9], [4, 4, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].

MATHEMATICA

nmax = 70; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}] - Product[1/(1 + x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A000290, A001156, A027193, A292520, A339364, A339366, A339367.

Sequence in context: A247856 A059660 A194003 * A035456 A035664 A095246

Adjacent sequences:  A339362 A339363 A339364 * A339366 A339367 A339368

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 01 2020

STATUS

approved

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Last modified September 27 18:30 EDT 2021. Contains 347694 sequences. (Running on oeis4.)