A175372 - OEIS

%I #40 Sep 08 2022 08:45:51

%S 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 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 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 Number of integer pairs (x,y) satisfying x^4 + y^4 = n.

%C A 4th-power variant of A004018 and A175362.

%C a(n) is nonzero when n appears in A004831. a(n) > 8 when n appears in A003824. - _Mason Korb_, Oct 06 2018

%H G. C. Greubel, <a href="/A175372/b175372.txt">Table of n, a(n) for n = 0..10000</a>

%H 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 G.f.: (1 + 2*Sum_{j>=1} x^(j^4))^2.

%p 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 CoefficientList[Series[(1 + 2*Sum[x^(j^4), {j, 1, 100}])^2, {x, 0, 120}], x] (* _G. C. Greubel_, Oct 06 2018 *)

%o (PARI) x='x+O('x^120); Vec((1+2*sum(j=1,50, x^(j^4)))^2) \\ _G. C. Greubel_, Oct 06 2018

%o (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 Cf. A004018, A175362.

%Y Cf. A003824, A004831 (where a(n) is nonzero).

%K nonn

%O 0,2

%A _R. J. Mathar_, Apr 24 2010