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A361431 Number of ways to write n^2 as an ordered sum of n^2 squares of integers.

%I A361431 #9 Mar 13 2023 09:17:01
%S A361431 1,2,24,34802,509145568,142743029326162,715761543475698773496,
%T A361431 63014651062141097287201438690,96683719664587866428237173383906926464,
%U A361431 2573179910450886540215919614478751310457090316706,1184101051443285881265166362742300236491599013268534224381864
%N A361431 Number of ways to write n^2 as an ordered sum of n^2 squares of integers.
%H A361431 Alois P. Heinz, <a href="/A361431/b361431.txt">Table of n, a(n) for n = 0..40</a>
%F A361431 a(n) = [x^(n^2)] (Sum_{j=-oo..oo} x^(j^2))^(n^2).
%F A361431 a(n) = A066535(n^2).
%e A361431 a(2) = 24: 4 = x^2 + y^2 + z^2 + u^2 has 24 solutions (x,y,z,u): 16 permutations of (+/-1,+/-1,+/-1,+/-1) and 8 permutations of (+/-2,0,0,0).
%p A361431 b:= proc(n, t) option remember; `if`(n=0, 1, `if`(n<0 or t<1, 0,
%p A361431       b(n, t-1) +2*add(b(n-j^2, t-1), j=1..isqrt(n))))
%p A361431     end:
%p A361431 a:= n-> b(n^2$2):
%p A361431 seq(a(n), n=0..10);
%Y A361431 Cf. A000290, A066535.
%K A361431 nonn
%O A361431 0,2
%A A361431 _Alois P. Heinz_, Mar 11 2023