A257021 Numbers whose quarter-square representation consists of four terms.

255, 271, 287, 304, 321, 339, 357, 376, 395, 399, 415, 419, 435, 439, 456, 460, 477, 481, 499, 503, 521, 525, 544, 548, 567, 571, 575, 591, 595, 599, 615, 619, 623, 640, 644, 648, 665, 669, 673, 691, 695, 699, 717, 721, 725, 744, 748, 752, 771, 775, 779, 799

Offset: 1

Author

Clark Kimberling, Apr 15 2015

Keywords

• nonn
• easy

Comments

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

Examples

			Quarter-square representations:
r(255) = 240 + 12 + 2 + 1; four terms
r(6969) = 6889 + 72 + 6 + 2; four terms
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002620, A257019, A257020, A257023.

Programs

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]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];
u = Table[Length[r[n]], {n, 0, 4 z}];(* A257023 *)
Flatten[-1 + Position[u, 1]]; (* A002620 *)
Flatten[-1 + Position[u, 2]]; (* A257019 *)
Flatten[-1 + Position[u, 3]]; (* A257020 *)
Flatten[-1 + Position[u, 4]]; (* A257021 *)