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A256915 Length of the enhanced squares representation of n.

%I A256915 #8 Apr 15 2015 13:30:43
%S A256915 1,1,1,1,1,2,2,2,3,1,2,2,2,2,3,3,1,2,2,2,2,3,3,3,4,1,2,2,2,2,3,3,3,4,
%T A256915 2,3,1,2,2,2,2,3,3,3,4,2,3,3,3,1,2,2,2,2,3,3,3,4,2,3,3,3,3,4,1,2,2,2,
%U A256915 2,3,3,3,4,2,3,3,3,3,4,4,2,1,2,2,2,2
%N A256915 Length of the enhanced squares representation of n.
%C A256915 See A256913 for definitions.
%H A256915 Clark Kimberling, <a href="/A256915/b256915.txt">Table of n, a(n) for n = 0..1000</a>
%e A256915 R(0) = 0, so length = 1.
%e A256915 R(1) = 1, so length = 1.
%e A256915 R(8) = 4 + 3 + 1, so length = 3.
%e A256915 R(7224) = 7056 + 144 + 16 + 4 + 3 + 1, so length = 6.
%t A256915 b[n_] := n^2; bb = Insert[Table[b[n], {n, 0, 100}]  , 2, 3];
%t A256915 s[n_] := Table[b[n], {k, 1, 2 n + 1}];
%t A256915 h[1] = {0, 1, 2, 3}; h[n_] := Join[h[n - 1], s[n]];
%t A256915 g = h[100]; Take[g, 100]
%t A256915 r[0] = {0}; r[1] = {1}; r[2] = {2}; r[3] = {3}; r[8] = {4, 3, 1};
%t A256915 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];
%t A256915 t = Table[r[n], {n, 0, 120}] (* A256913, before concatenation *)
%t A256915 Flatten[t]  (* A256913 *)
%t A256915 Table[Last[r[n]], {n, 0, 120}]    (* A256914 *)
%t A256915 Table[Length[r[n]], {n, 0, 200}]  (* A256915 *)
%o A256915 (Haskell)
%o A256915 a256915 = length . a256913_row  -- _Reinhard Zumkeller_, Apr 15 2015
%Y A256915 Cf. A000290, A256913, A256914 (trace).
%Y A256915  Cf. A257071.
%K A256915 nonn,easy
%O A256915 0,6
%A A256915 _Clark Kimberling_, Apr 14 2015