A257019 Numbers whose quarter-square representation consists of two terms.

3, 5, 7, 8, 10, 11, 13, 14, 17, 18, 21, 22, 24, 26, 27, 29, 31, 32, 34, 37, 38, 40, 43, 44, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 65, 66, 68, 70, 73, 74, 76, 78, 82, 83, 85, 87, 91, 92, 94, 96, 99, 101, 102, 104, 106, 109, 111, 112, 114, 116, 119, 122, 123

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(0) = 0, one term
r(1) = 1, one term
r(3) = 2 + 1, two terms, so a(1) = 3

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, A257020, A257021, A257023.

Sequence in context: A049068 A185602 A225554 * A071977 A183423 A109404

Adjacent sequences: A257016 A257017 A257018 * A257020 A257021 A257022

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2015

Status

approved