OFFSET
1,1
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
Quarter-square representations:
r(0) = 0
r(1) = 1
r(2) = 2, so that a(1) = 2
r(3) = 2 + 1
r(4) = 4
r(5) = 4 + 1
r(6) = 6, so that a(2) = 6
MATHEMATICA
z = 400; 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]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];
u = Table[Length[r[n]], {n, 0, z}] (* A257023 *)
v = Table[Length[Intersection[r[n], Table[n^2, {n, 0, 1000}]]], {n, 0, z}] (* A257024 *)
-1 + Select[Range[0, z], 2 v[[#]] < u[[#]] &] (* A257056 *)
-1 + Select[Range[0, z], 2 v[[#]] == u[[#]] &] (* A257057 *)
-1 + Select[Range[0, z], 2 v[[#]] > u[[#]] &] (* A257058 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 15 2015
STATUS
approved