A256796 Positive part of the minimal alternating squares representation of n.

1, 4, 4, 4, 9, 10, 11, 9, 9, 20, 20, 16, 17, 18, 16, 16, 26, 29, 29, 29, 25, 26, 27, 25, 25, 46, 36, 37, 40, 40, 40, 36, 37, 38, 36, 36, 53, 58, 59, 49, 50, 53, 53, 53, 49, 50, 51, 49, 49, 68, 68, 68, 73, 74, 64, 65, 68, 68, 68, 64, 65, 66, 64, 64, 81, 82

Offset

1,2

Comments

See A256789 for definitions.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A256789, A256797.

Sequence in context: A048761 A211547 A075561 * A117405 A013601 A219802

Adjacent sequences: A256793 A256794 A256795 * A256797 A256798 A256799

Keyword

nonn,easy

Author

Clark Kimberling, Apr 13 2015

Status

approved