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

%I A256790 #6 Apr 14 2015 11:04:34
%S A256790 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,
%T A256790 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,
%U A256790 4,3,4,5,2,3,4,4,3,2,3,3,2,1,5,4,2,3
%N A256790 Number of terms in the minimal alternating squares representation of n.
%C A256790 See A256789 for definitions.
%H A256790 Clark Kimberling, <a href="/A256790/b256790.txt">Table of n, a(n) for n = 0..1000</a>
%e A256790 R(0) = 0, so a(0) = 1;
%e A256790 R(1) = 1, so a(1) = 1;
%e A256790 R(2) = 4 - 2, so a(2) = 2;
%e A256790 R(7) = 9 - 4 + 2, so a(7) = 3;
%e A256790 R(89) = 100 - 16 + 9 - 4, so a(89) = 4.
%t A256790 b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];
%t A256790 s[n_] := Table[b[n], {k, 1, 2 n - 1}];
%t A256790 h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
%t A256790 g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
%t A256790 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256790 Table[r[n], {n, 0, 120}] (* A256789 *)
%t A256790 Flatten[Table[Length[r[n]], {n, 0, 1000}]]  (* A256790 *)
%Y A256790 Cf. A256789.
%K A256790 nonn,easy
%O A256790 0,3
%A A256790 _Clark Kimberling_, Apr 13 2015