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.
%I A175372 #40 Sep 08 2022 08:45:51 %S A175372 1,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,4,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0, %T A175372 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %U A175372 0,0,0,0,0,0,0,0,0,0,0,0,0,4,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0 %N A175372 Number of integer pairs (x,y) satisfying x^4 + y^4 = n. %C A175372 A 4th-power variant of A004018 and A175362. %C A175372 a(n) is nonzero when n appears in A004831. a(n) > 8 when n appears in A003824. - _Mason Korb_, Oct 06 2018 %H A175372 G. C. Greubel, <a href="/A175372/b175372.txt">Table of n, a(n) for n = 0..10000</a> %H A175372 M. Korb, <a href="https://math.stackexchange.com/questions/2837316/whats-the-connection-between-theta-series-and-the-number-of-integer-solution">What's the connection between theta series and the number of integer solutions on a curve? </a>, Math StackExchange, July 2018. %F A175372 G.f.: (1 + 2*Sum_{j>=1} x^(j^4))^2. %p A175372 seq(coeff(series((1+2*add(x^(j^4),j=1..n))^2,x,n+1), x, n), n = 0 .. 120); # _Muniru A Asiru_, Oct 07 2018 %t A175372 CoefficientList[Series[(1 + 2*Sum[x^(j^4), {j, 1, 100}])^2, {x, 0, 120}], x] (* _G. C. Greubel_, Oct 06 2018 *) %o A175372 (PARI) x='x+O('x^120); Vec((1+2*sum(j=1,50, x^(j^4)))^2) \\ _G. C. Greubel_, Oct 06 2018 %o A175372 (Magma) m:=120; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*(&+[x^(j^4): j in [1..50]]))^2)); // _G. C. Greubel_, Oct 06 2018 %Y A175372 Cf. A004018, A175362. %Y A175372 Cf. A003824, A004831 (where a(n) is nonzero). %K A175372 nonn %O A175372 0,2 %A A175372 _R. J. Mathar_, Apr 24 2010