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Number of ordered ways of writing n as a sum of 4 squares of nonnegative integers.
11

%I #15 May 16 2023 07:14:39

%S 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,

%T 42,28,12,36,48,16,6,36,42,36,29,28,48,28,18,48,60,28,24,60,48,24,8,

%U 44,72,48,30,48,84,36,24,52,54

%N Number of ordered ways of writing n as a sum of 4 squares of nonnegative integers.

%C 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

%H T. D. Noe, <a href="/A014110/b014110.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F 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.

%e 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

%Y Convolution square of A000925.

%K easy,nonn

%O 0,2

%A Joe Keane (jgk(AT)jgk.org)