A256796 - OEIS

%I #14 May 14 2017 11:51:37

%S 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,

%T 46,36,37,40,40,40,36,37,38,36,36,53,58,59,49,50,53,53,53,49,50,51,49,

%U 49,68,68,68,73,74,64,65,68,68,68,64,65,66,64,64,81,82

%N Positive part of the minimal alternating squares representation of n.

%C See A256789 for definitions.

%H Clark Kimberling, <a href="/A256796/b256796.txt">Table of n, a(n) for n = 1..1000</a>

%e R(1) = 1, positive part 1, nonpositive part 0;

%e R(2) = 4 - 2, positive part 4, nonpositive part 2;

%e R(3) = 4 - 1, positive part 4, nonpositive part 1;

%e R(89) = 100 - 16 + 9 - 4, positive part 100 + 9 = 109, nonpositive part 16 + 4 = 20.

%t b[n_] := n^2; bb = Table[b[n], {n, 0, 100}];

%t s[n_] := Table[b[n], {k, 1, 2 n - 1}];

%t h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];

%t g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};

%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];

%t t = Table[r[n], {n, 1, z}] (* A256789 *)

%t Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256796 *)

%t Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256797 *)

%Y Cf. A256789, A256797.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Apr 13 2015