A339366 Number of partitions of n into an even number of distinct squares.

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

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