%I
%S 1,1,0,1,1,2,0,1,0,1,2,1,0,1,0,1,1,2,1,2,0,1,0,1,1,1,2,1,2,2,0,1,0,1,
%T 1,2,1,2,1,2,2,3,0,1,0,1,1,2,0,1,2,1,2,2,3,1,0,1,0,1,1,2,0,1,1,2,1,2,
%U 2,3,1,2,0,1,0,1,1,2,0,1,0,1,2,1,2,2
%N Number of squares in the quartersum representation of n.
%C Every positive integer is a sum of at most four distinct quarter squares; see A257019.
%H Clark Kimberling, <a href="/A257024/b257024.txt">Table of n, a(n) for n = 0..1000</a>
%e Quartersquare representations:
%e r(5) = 4 + 1, so a(5) = 2;
%e r(11) = 9 + 2, so a(11) = 1;
%e r(35) = 30 + 4 + 1, so a(35) = 2.
%t z = 100; b[n_] := Floor[(n + 1)^2/4]; bb = Table[b[n], {n, 0, 100}];
%t s[n_] := Table[b[n], {k, b[n + 1]  b[n]}];
%t h[1] = {1}; h[n_] := Join[h[n  1], s[n]];
%t g = h[100]; Take[g, 100]; r[0] = {0};
%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n  g[[n]]]]]
%t sq = Table[n^2, {n, 0, 1000}]; t = Table[r[n], {n, 0, z}]
%t u = Table[Length[Intersection[r[n], sq]], {n, 0, 250}]
%Y Cf. A002620, A257019, A257020, A257021, A257022.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 15 2015
