A287617 Main diagonal of A045847.

1, 1, 1, 1, 5, 21, 61, 141, 309, 766, 2191, 6436, 18041, 48348, 128311, 347166, 960197, 2674883, 7413514, 20411986, 56130675, 154907229, 429349768, 1192532452, 3312339849, 9196063371, 25538113056, 70994900341, 197595884071, 550414483911, 1533911418946

Offset

0,5

Comments

a(n) is the number of representations of n as a sum of n squares of nonnegative integers.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..500

Formula

a(n) = [x^n] (1 + theta_3(x))^n/2^n, where theta_() is the Jacobi theta function. - Ilya Gutkovskiy, Jan 17 2018

a(n) ~ c * d^n / sqrt(n), where d = 2.83312434251238... and c = 0.229098651125... - Vaclav Kotesovec, Mar 25 2023

Crossrefs

Cf. A045847.

Sequence in context: A203233 A112561 A303170 * A354551 A143567 A147375

Adjacent sequences: A287614 A287615 A287616 * A287618 A287619 A287620

Keyword

nonn

Author

Seiichi Manyama, May 28 2017

Status

approved