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

%I A256797 #11 May 14 2017 11:51:48
%S A256797 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,
%T A256797 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,
%U A256797 4,4,4,1,0,16,16,18,17,16,20,20,9,9,11,10,9,4
%N A256797 Nonpositive part of the minimal alternating squares representation of n.
%C A256797 See A256789 for definitions.
%H A256797 Clark Kimberling, <a href="/A256797/b256797.txt">Table of n, a(n) for n = 1..1000</a>
%e A256797 R(1) = 1, positive part 1, nonpositive part 0;
%e A256797 R(2) = 4 - 2, positive part 4, nonpositive part 2;
%e A256797 R(3) = 4 - 1, positive part 4, nonpositive part 1;
%e A256797 R(89) = 100 - 16 + 9 - 4, positive part 100 + 9 = 109, nonpositive part 16 + 4 = 20.
%t A256797 b[n_] := n^2; bb = Table[b[n], {n, 0, 100}];
%t A256797 s[n_] := Table[b[n], {k, 1, 2 n - 1}];
%t A256797 h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
%t A256797 g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
%t A256797 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256797 t = Table[r[n], {n, 1, z}] (* A256789 *)
%t A256797 Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256796 *)
%t A256797 Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256797 *)
%Y A256797 Cf. A256789, A256796.
%K A256797 nonn,easy
%O A256797 1,2
%A A256797 _Clark Kimberling_, Apr 13 2015