OFFSET
0,6
COMMENTS
Every positive integer is a sum of at most four distinct quarter squares; see A257019.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
EXAMPLE
Quarter-square representations:
r(5) = 4 + 1, so a(5) = 2;
r(11) = 9 + 2, so a(11) = 1;
r(35) = 30 + 4 + 1, so a(35) = 2.
MATHEMATICA
z = 100; b[n_] := Floor[(n + 1)^2/4]; bb = Table[b[n], {n, 0, 100}];
s[n_] := Table[b[n], {k, b[n + 1] - b[n]}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; Take[g, 100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]]
sq = Table[n^2, {n, 0, 1000}]; t = Table[r[n], {n, 0, z}]
u = Table[Length[Intersection[r[n], sq]], {n, 0, 250}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 15 2015
STATUS
approved