OFFSET
0,2
COMMENTS
Conjecture: a(n) > 0 except for n = 46.
It seems that the only values of n > 500 with a(n) = 1 are 586, 616, 1097, 1208, 3496, 3736, 4486, 21736, 24568, 37870.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 0..10000
EXAMPLE
a(115) = 1 with 115 = 5^2 + 3*3^2 + 1^4 + 2*2^4 + 5*3*1*2.
a(1097) = 1 with 1097 = 29^2 + 3*0^2 + 4^4 + 2*0^4 + 29*0*4*0.
a(4468) = 1 with 4468 = 5^2 + 3*21^2 + 7^4 + 2*1^4 + 5*21*7*1.
a(21736) = 1 with 21736 = 50^2 + 3*65^2 + 9^4 + 2*0^4 + 50*65*9*0.
a(24568) = 1 with 24568 = 121^2 + 3*3^2 + 2^4 + 2*7^4 + 121*3*2*7.
a(37870) = 1 with 37870 = 31^2 + 3*27^2 + 5^4 + 2*7^4 + 31*27*5*7.
MATHEMATICA
SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]];
tab={}; Do[r=0; Do[If[SQ[4(n-2w^4-z^4-3*y^2)+(y*z*w)^2], r=r+1], {w, 0, (n/2)^(1/4)}, {z, 0, (n-2w^4)^(1/4)}, {y, 0, Sqrt[(n-2w^4-z^4)/3]}]; tab=Append[tab, r], {n, 0, 100}]; Print[tab]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Mar 25 2022
STATUS
approved