A256797 Nonpositive part of the minimal alternating squares representation of n.

0, 2, 1, 0, 4, 4, 4, 1, 0, 10, 9, 4, 4, 4, 1, 0, 9, 11, 10, 9, 4, 4, 4, 1, 0, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 16, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4

Offset: 1

Author

Clark Kimberling, Apr 13 2015

Keywords

• nonn
• easy

Comments

See A256789 for definitions.

Examples

			R(1) = 1, positive part 1, nonpositive part 0;
R(2) = 4 - 2, positive part 4, nonpositive part 2;
R(3) = 4 - 1, positive part 4, nonpositive part 1;
R(89) = 100 - 16 + 9 - 4, positive part 100 + 9 = 109, nonpositive part 16 + 4 = 20.
		

Links

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

Crossrefs

Cf. A256789, A256796.

Programs

Mathematica

b[n_] := n^2; bb = Table[b[n], {n, 0, 100}];
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]]];
t = Table[r[n], {n, 1, z}] (* A256789 *)
Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256796 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256797 *)