A257019 - OEIS

%I #4 Apr 15 2015 15:42:26

%S 3,5,7,8,10,11,13,14,17,18,21,22,24,26,27,29,31,32,34,37,38,40,43,44,

%T 46,48,50,51,53,55,57,58,60,62,65,66,68,70,73,74,76,78,82,83,85,87,91,

%U 92,94,96,99,101,102,104,106,109,111,112,114,116,119,122,123

%N Numbers whose quarter-square representation consists of two terms.

%C Every positive integer is a sum of at most four distinct quarter squares (see A257019).

%H Clark Kimberling, <a href="/A257019/b257019.txt">Table of n, a(n) for n = 1..1000</a>

%e Quarter-square representations:

%e r(0) = 0, one term

%e r(1) = 1, one term

%e r(3) = 2 + 1, two terms, so a(1) = 3

%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]; r[0] = {0};

%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];

%t u = Table[Length[r[n]], {n, 0, 4 z}];(* A257023 *)

%t Flatten[-1 + Position[u, 1]]; (* A002620 *)

%t Flatten[-1 + Position[u, 2]]; (* A257019 *)

%t Flatten[-1 + Position[u, 3]]; (* A257020 *)

%t Flatten[-1 + Position[u, 4]]; (* A257021 *)

%Y Cf. A002620, A257020, A257021, A257023.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Apr 15 2015