OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Olivia X. M. Yao, Ernest X. W. Xia, Combinatorial proofs of five formulas of Liouville, Discrete Math. 318 (2014), 1--9. MR3141622.
FORMULA
Yao and Xia give an explicit formula for a(n) due to Liouville.
G.f.: theta_3(q)*theta_3(q^2)^2*theta_3(q^4), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 03 2018
MAPLE
with(LinearAlgebra);
L:=proc(a, b, c, d, M) local n, hit, ul, vl, wl, xl, u, v, w, x, su, sv, sw, sx;
hit:=Array(0..M); ul:=floor(sqrt(M/a)); vl:=floor(sqrt(M/b));
wl:=floor(sqrt(M/c)); xl:=floor(sqrt(M/d));
for u from -ul to ul do
su:=a*u^2;
for v from -vl to vl do
sv:=su+b*v^2;
for w from -wl to wl do
sw:=sv+c*w^2;
for x from -xl to xl do
sx:=sw+d*x^2;
if sx <= M then hit[sx]:=hit[sx]+1; fi;
od; od; od; od;
[seq(hit[n], n=0..M)];
end;
L(1, 2, 2, 4, 60);
MATHEMATICA
CoefficientList[EllipticTheta[3, 0, q]*EllipticTheta[3, 0, q^2]^2*EllipticTheta[3, 0, q^4] + O[q]^100, q] (* Jean-François Alcover, Feb 15 2023, after Ilya Gutkovskiy *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 14 2014
STATUS
approved