The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A256914

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A256914

Trace of the enhanced squares representation of n.
(history; published version)

#10 by Reinhard Zumkeller at Wed Apr 15 13:30:56 EDT 2015

STATUS

editing

approved

#9 by Reinhard Zumkeller at Wed Apr 15 13:06:31 EDT 2015

CROSSREFS

Cf. A257046, A257047, A257070.

STATUS

approved

editing

#8 by Reinhard Zumkeller at Wed Apr 15 04:56:34 EDT 2015

STATUS

editing

approved

#7 by Reinhard Zumkeller at Wed Apr 15 04:56:17 EDT 2015

COMMENTS

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

CROSSREFS

Cf. A257046, A257047.

STATUS

approved

editing

#6 by Reinhard Zumkeller at Wed Apr 15 04:17:46 EDT 2015

STATUS

editing

approved

#5 by Reinhard Zumkeller at Wed Apr 15 04:10:43 EDT 2015

PROG

(Haskell)

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

STATUS

approved

editing

#4 by N. J. A. Sloane at Tue Apr 14 16:44:40 EDT 2015

STATUS

proposed

approved

#3 by Clark Kimberling at Tue Apr 14 15:39:26 EDT 2015

STATUS

editing

proposed

#2 by Clark Kimberling at Tue Apr 14 12:13:42 EDT 2015

NAME

allocated for Clark KimberlingTrace of the enhanced squares representation of n.

DATA

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.

LINKS

Clark Kimberling, <a href="/A256914/b256914.txt">Table of n, a(n) for n = 0..1000</a>

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 *)

CROSSREFS

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

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Apr 14 2015

STATUS

approved

editing

#1 by Clark Kimberling at Sun Apr 12 16:23:03 EDT 2015

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved