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A256914 Trace of the enhanced squares representation of n. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 16 20:09 EST 2019. Contains 329206 sequences. (Running on oeis4.)