A257020 - OEIS

%I #4 Apr 15 2015 15:42:47

%S 15,19,23,28,33,35,39,41,45,47,52,54,59,61,63,67,69,71,75,77,79,80,84,

%T 86,88,89,93,95,97,98,103,105,107,108,113,115,117,118,120,124,126,128,

%U 129,131,135,137,139,140,142,143,147,149,151,152,154,155,159,161

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

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

%H Clark Kimberling, <a href="/A257020/b257020.txt">Table of n, a(n) for n = 1..1000</a>

%e Quarter-square representations:

%e r(15) = 12 + 2 + 1, three terms; a(1) = 15

%e r(19) = 16 + 2 + 1, three terms; a(2) = 19

%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, A257019, A257021, A257023 (trace), A257024 (number of square in quarter-square representation).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Apr 15 2015