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

Author

Seiichi Manyama, May 28 2017

Keywords

• nonn

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

Crossrefs

Cf. A045847.

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