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A014110
Number of ordered ways of writing n as a sum of 4 squares of nonnegative integers.
11
1, 4, 6, 4, 5, 12, 12, 4, 6, 16, 18, 12, 8, 16, 24, 12, 5, 24, 30, 16, 18, 28, 24, 12, 12, 28, 42, 28, 12, 36, 48, 16, 6, 36, 42, 36, 29, 28, 48, 28, 18, 48, 60, 28, 24, 60, 48, 24, 8, 44, 72, 48, 30, 48, 84, 36, 24, 52, 54
OFFSET
0,2
COMMENTS
This counts ordered sums of squares of nonnegative integers, whereas A000118 counts ordered sums of squares of integers of any sign. - R. J. Mathar, May 16 2023
FORMULA
Coefficient of q^n in (1/16)*(1 + theta_3(0, q))^4; or coeff. of q^n in (Sum q^(i^2), i=0..inf)^4.
EXAMPLE
a(1)=4 counts 0^2+0^2+0^2+1^2 = 0^2+0^2+1^2+0^2 = 0^2+1^2+0^2+0^2 = 1^2+0^2+0^2+0^2. a(2)=6 counts 0^2+0^2+1^2+1^2 = 0^2+1^2+0^2+1^2 = 0^2+1^2+1^2+0^2 = 1^2+0^2+0^2+1^2 = 1^2+0^2+1^2+0^2 = 1^2+1^2+0^2+0^2. - R. J. Mathar, May 16 2023
CROSSREFS
Convolution square of A000925.
Sequence in context: A092039 A243371 A123999 * A266491 A323016 A261637
KEYWORD
easy,nonn
AUTHOR
Joe Keane (jgk(AT)jgk.org)
STATUS
approved