A256790 Number of terms in the minimal alternating squares representation of n.

1, 1, 2, 2, 1, 2, 3, 3, 2, 1, 4, 3, 2, 3, 3, 2, 1, 3, 4, 4, 3, 2, 3, 3, 2, 1, 5, 2, 3, 4, 4, 3, 2, 3, 3, 2, 1, 3, 4, 5, 2, 3, 4, 4, 3, 2, 3, 3, 2, 1, 4, 4, 3, 4, 5, 2, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 3, 4, 4, 3, 4, 5, 2, 3, 4, 4, 3, 2, 3, 3, 2, 1, 5, 4, 2, 3

Offset: 0

Author

Clark Kimberling, Apr 13 2015

Keywords

• nonn
• easy

Comments

See A256789 for definitions.

Examples

			R(0) = 0, so a(0) = 1;
R(1) = 1, so a(1) = 1;
R(2) = 4 - 2, so a(2) = 2;
R(7) = 9 - 4 + 2, so a(7) = 3;
R(89) = 100 - 16 + 9 - 4, so a(89) = 4.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A256789.

Programs

Mathematica

b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];
s[n_] := Table[b[n], {k, 1, 2 n - 1}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[r[n], {n, 0, 120}] (* A256789 *)
Flatten[Table[Length[r[n]], {n, 0, 1000}]]  (* A256790 *)