A256915 Length of the enhanced squares representation of n.

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, 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, 2, 3, 3, 3, 4, 2, 3, 3, 3, 3, 4, 4, 2, 1, 2, 2, 2, 2

Offset

0,6

Comments

See A256913 for definitions.

Links

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

Example

R(0) = 0, so length = 1.
R(1) = 1, so length = 1.
R(8) = 4 + 3 + 1, so length = 3.
R(7224) = 7056 + 144 + 16 + 4 + 3 + 1, so length = 6.

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)
a256915 = length . a256913_row  -- Reinhard Zumkeller, Apr 15 2015

Crossrefs

Cf. A000290, A256913, A256914 (trace).

Cf. A257071.

Sequence in context: A139465 A010244 A141298 * A348367 A209254 A227738

Adjacent sequences: A256912 A256913 A256914 * A256916 A256917 A256918

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2015

Status

approved