OFFSET
1,5
COMMENTS
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, Refining Lagrange's four-square theorem, J. Number Theory 175(2017), 167-190.
Zhi-Wei Sun, New conjectures on representations of integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), no. 2, 97-120.
Zhi-Wei Sun, Restricted sums of four squares, arXiv:1701.05868 [math.NT], 2017-2018.
EXAMPLE
a(4) = 1 with 4 = 0^2 + 5*0^2 + 2^0 + 3*2^0.
a(5) = 2 with 5 = 1^2 + 5*0^2 + 2^0 + 3*2^0 = 0^2 + 5*0^2 + 2^1 + 3*2^0.
a(6) = 1 with 6 = 1^2 + 3*0^2 + 2^1 + 3*2^0.
MATHEMATICA
SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]];
tab={}; Do[r=0; Do[If[SQ[n-3*2^k-2^j-5x^2], r=r+1], {k, 0, Log[2, n/3]}, {j, 0, If[n==3*2^k, -1, Log[2, n-3*2^k]]}, {x, 0, Sqrt[(n-3*2^k-2^j)/5]}]; tab=Append[tab, r], {n, 1, 60}]; Print[tab]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Apr 16 2018
STATUS
approved