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Number of solutions to a^2 + b^2 + 4*c^2 = n.
3

%I #6 Aug 01 2018 10:30:00

%S 1,4,4,0,6,16,8,0,12,20,8,0,8,16,16,0,6,32,12,0,24,32,8,0,24,20,24,0,

%T 0,48,16,0,12,32,16,0,30,16,24,0,24,64,16,0,24,48,16,0,8,36,28,0,24,

%U 48,32,0,48,32,8,0,0,48,32,0,6,64,32,0,48,64,16,0,36,32,40,0,24,64,16,0,24,68

%N Number of solutions to a^2 + b^2 + 4*c^2 = n.

%F G.f.: theta_3(q)^2*theta_3(q^4), where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Aug 01 2018

%p t0:=Array(0..10000,0); M:=15;

%p for i from -M to M do for j from -M to M do for k from -M to M do

%p t1:=i^2+j^2+4*k^2; t0[t1]:=t0[t1]+1; od: od: od:

%p [seq(t0[i],i=0..100)];

%Y x^2+y^2+k*z^2: A005875, A014455, A034933, A169784.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, May 12 2010