A339364 Number of partitions of n into an even number of squares.

1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 3, 1, 3, 3, 3, 3, 4, 4, 6, 4, 7, 6, 7, 7, 8, 9, 11, 9, 13, 12, 14, 14, 16, 16, 20, 17, 23, 22, 25, 25, 28, 29, 33, 31, 37, 38, 41, 42, 45, 48, 54, 51, 61, 60, 67, 67, 72, 76, 84, 81, 93, 93, 102, 104, 110, 117, 125, 125, 139, 140, 153

Offset

0,9

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(10) = 3 because we have [9, 1], [4, 4, 1, 1] and [1, 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, A027187, A292520, A339365, A339366, A339367.

Sequence in context: A368290 A111248 A100714 * A050123 A081386 A213712

Adjacent sequences: A339361 A339362 A339363 * A339365 A339366 A339367

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 01 2020

Status

approved