A256914 Trace of the enhanced squares representation of n.

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, 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, 2, 3, 4, 1, 2, 3, 1, 9, 1, 2, 3, 4, 1, 2, 16, 81, 1, 2

Offset: 0

Author

Clark Kimberling, Apr 14 2015

Keywords

• nonn
• easy

Comments

See A256913 for definitions.

a(A257046(n)) = 1; a(A257047(n)) != 1. - Reinhard Zumkeller, Apr 15 2015

Examples

			R(0) = 0, so trace = 0.
R(1) = 1, so trace = 1.
R(8) = 4 + 3 + 1, so trace = 1.
R(43) = 36 + 4 + 3, so trace = 3.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000290, A256913, A256915 (number of terms).

Cf. A257046, A257047, A257070.

Programs

Haskell

a256914 = last . a256913_row  -- Reinhard Zumkeller, Apr 15 2015

Mathematica

b[n_] := n^2; bb = Insert[Table[b[n], {n, 0, 100}]  , 2, 3];
s[n_] := Table[b[n], {k, 1, 2 n + 1}];
h[1] = {0, 1, 2, 3}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; Take[g, 100]
r[0] = {0}; r[1] = {1}; r[2] = {2}; r[3] = {3}; r[8] = {4, 3, 1};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];
t = Table[r[n], {n, 0, 120}] (* A256913, before concatenation *)
Flatten[t]  (* A256913 *)
Table[Last[r[n]], {n, 0, 120}]    (* A256914 *)
Table[Length[r[n]], {n, 0, 200}]  (* A256915 *)