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

0,3

Comments

See A256913 for definitions.

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Cf. A257046, A257047, A257070.

Sequence in context: A078978 A322424 A309198 * A171171 A159957 A053840

Adjacent sequences: A256911 A256912 A256913 * A256915 A256916 A256917

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2015

Status

approved