cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A374493 Number of ways of writing n^2 as a sum of 8 squares.

This page as a plain text file.
%I A374493 #19 Aug 21 2025 09:59:35
%S A374493 1,16,1136,12112,74864,252016,859952,1887888,4793456,8830096,17893136,
%T A374493 28366288,56672048,77264112,134040048,190776112,306783344,386279728,
%U A374493 626936816,752843856,1179182864,1429131216,2014006448,2368768912,3628646192,3937752016,5485751952
%N A374493 Number of ways of writing n^2 as a sum of 8 squares.
%H A374493 Paolo Xausa, <a href="/A374493/b374493.txt">Table of n, a(n) for n = 0..10000</a>
%H A374493 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A374493 a(n) = [x^(n^2)] (Sum_{j=-n..n} x^(j^2))^8.
%F A374493 a(n) = A000143(n^2).
%F A374493 a(n) is divisible by 16 for n > 0.
%t A374493 SquaresR[8, Range[0,30]^2] (* _Paolo Xausa_, Aug 21 2025 *)
%o A374493 (PARI) a000143(n) = if(n==0, 1, 16*sumdiv(n, d, (-1)^(n+d)*d^3));
%o A374493 a(n) = a000143(n^2);
%Y A374493 Column k=8 of A302996.
%Y A374493 Cf. A000143.
%K A374493 nonn
%O A374493 0,2
%A A374493 _Seiichi Manyama_, Jul 12 2024