

A236933


Number of integer solutions to a^2 + b^2 + c^2 + 12*d^2 = n.


10



1, 6, 12, 8, 6, 24, 24, 0, 12, 30, 24, 24, 10, 36, 72, 16, 18, 96, 84, 24, 48, 108, 72, 48, 40, 78, 168, 32, 12, 168, 120, 48, 60, 144, 96, 48, 78, 84, 216, 64, 24, 240, 144, 24, 48, 168, 144, 96, 70, 114, 252, 64, 84, 312, 240, 48, 120, 252, 168, 120, 32
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OFFSET

0,2


LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000


FORMULA

G.f.: theta_3(q)^3*theta_3(q^12), where theta_3() is the Jacobi theta function.  Ilya Gutkovskiy, Aug 03 2018


MAPLE

See A236924.


CROSSREFS

Different from A005875.
For number of solutions to a^2+b^2+c^2+k*d^2=n for k=1,2,3,4,5,6,7,8,12 see A000118, A236928, A236926, A236923, A236930, A236931, A236932, A236927, A236933.
Sequence in context: A105730 A213384 A005875 * A236927 A236932 A281484
Adjacent sequences: A236930 A236931 A236932 * A236934 A236935 A236936


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Feb 16 2014


STATUS

approved



