OFFSET
0,10
COMMENTS
It was conjectured by Schmutz Schaller that B(x)>=B_3(x) for every x; this was proved in the reference given.
LINKS
P. Moree and H. J. J. te Riele, The hexagonal versus the square lattice, arXiv:math/0204332 [math.NT], 2002.
P. Moree and H. J. J. te Riele, The hexagonal versus the square lattice, Math. Comp. 73 (2004), no. 245, 451-473.
MAPLE
for j from 0 to 200 do; a[j] := 0; b[j] := 0; end do: for i from 0 to 15 do; for j from 0 to 15 do; u := i*i+j*j; v := i*i+3*j*j; if u<201 then a[u] := 1; end if; if v<201 then b[v] := 1; end if; end do; end do: u := 0: for j from 0 to 200 do; u := u+a[j]-b[j]; print(j, u); end do:
MATHEMATICA
max = 99; rmax = Floor[Sqrt[max]]; ClearAll[a, b]; a[_] = 0; b[_] = 0; Do[u = i*i + j*j; v = i*i + 3*j*j; If[u < max, a[u] = 1]; If[v < max, b[v] = 1], {i, 0, rmax}, {j, 0, rmax}]; Accumulate[ Array[a, max] - Array[b, max]] (* Jean-François Alcover, Oct 18 2011, after Maple *)
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
P. Moree (moree(AT)mpim-bonn.mpg.de), May 03 2002
STATUS
approved