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

1,1

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 = 1..1000

Example

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

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 *)

Crossrefs

Cf. A002620, A257019, A257020, A257023.

Sequence in context: A028526 A132828 A296899 * A359445 A306223 A023690

Adjacent sequences: A257018 A257019 A257020 * A257022 A257023 A257024

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2015

Status

approved