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A256914 Trace of the enhanced squares representation of n.

%I A256914 #10 Apr 15 2015 13:30:56
%S A256914 0,1,2,3,4,1,2,3,1,9,1,2,3,4,1,2,16,1,2,3,4,1,2,3,1,25,1,2,3,4,1,2,3,
%T A256914 1,9,1,36,1,2,3,4,1,2,3,1,9,1,2,3,49,1,2,3,4,1,2,3,1,9,1,2,3,4,1,64,1,
%U A256914 2,3,4,1,2,3,1,9,1,2,3,4,1,2,16,81,1,2
%N A256914 Trace of the enhanced squares representation of n.
%C A256914 See A256913 for definitions.
%C A256914 a(A257046(n)) = 1; a(A257047(n)) != 1. - _Reinhard Zumkeller_, Apr 15 2015
%H A256914 Clark Kimberling, <a href="/A256914/b256914.txt">Table of n, a(n) for n = 0..1000</a>
%e A256914 R(0) = 0, so trace = 0.
%e A256914 R(1) = 1, so trace = 1.
%e A256914 R(8) = 4 + 3 + 1, so trace = 1.
%e A256914 R(43) = 36 + 4 + 3, so trace = 3.
%t A256914 b[n_] := n^2; bb = Insert[Table[b[n], {n, 0, 100}]  , 2, 3];
%t A256914 s[n_] := Table[b[n], {k, 1, 2 n + 1}];
%t A256914 h[1] = {0, 1, 2, 3}; h[n_] := Join[h[n - 1], s[n]];
%t A256914 g = h[100]; Take[g, 100]
%t A256914 r[0] = {0}; r[1] = {1}; r[2] = {2}; r[3] = {3}; r[8] = {4, 3, 1};
%t A256914 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];
%t A256914 t = Table[r[n], {n, 0, 120}] (* A256913, before concatenation *)
%t A256914 Flatten[t]  (* A256913 *)
%t A256914 Table[Last[r[n]], {n, 0, 120}]    (* A256914 *)
%t A256914 Table[Length[r[n]], {n, 0, 200}]  (* A256915 *)
%o A256914 (Haskell)
%o A256914 a256914 = last . a256913_row  -- _Reinhard Zumkeller_, Apr 15 2015
%Y A256914 Cf. A000290, A256913, A256915 (number of terms).
%Y A256914 Cf. A257046, A257047, A257070.
%K A256914 nonn,easy
%O A256914 0,3
%A A256914 _Clark Kimberling_, Apr 14 2015