A108019 a(n) = (8^n - 1)*4/7.

0, 4, 36, 292, 2340, 18724, 149796, 1198372, 9586980, 76695844, 613566756, 4908534052, 39268272420, 314146179364, 2513169434916, 20105355479332, 160842843834660, 1286742750677284, 10293942005418276, 82351536043346212

Offset

0,2

Comments

Numbers n whose binary representation is 100, n times.

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (9,-8).

Formula

a(n) = 8*a(n-1) + 4 with n>0, a(0)=0. - Vincenzo Librandi, Nov 13 2010

From Colin Barker, Oct 15 2012: (Start)

a(n) = 9*a(n-1) - 8*a(n-2).

G.f.: 4*x/((x-1)*(8*x-1)). (End)

Example

a(3)=292 because 292 translated in base 2 is three times 100: 100100100.
From Zerinvary Lajos, Jan 14 2007: (Start)
Octal............Decimal
0......................0
4......................4
44....................36
444..................292
4444................2340
44444..............18724
444444............149796
4444444..........1198372
44444444.........9586980
444444444.......76695844
4444444444.....613566756,
etc. (End)

Mathematica

Table[ FromDigits[ Flatten[ Table[{1, 0, 0}, {i, n}]], 2], {n, 0, 19}] (* Robert G. Wilson v, Jun 01 2005 *)
s=0; lst={s}; Do[s+=2^n; AppendTo[lst, s], {n, 2, 5!, 3}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)
NestList[8#+4&, 0, 20] (* Harvey P. Dale, Aug 08 2013 *)

Prog

(PARI) a(n)=if(n<0, 0, (8^n-1)*4/7) /* Michael Somos */

Crossrefs

Cf. A020988.

Sequence in context: A277174 A059416 A240889 * A241104 A361554 A222428

Adjacent sequences: A108016 A108017 A108018 * A108020 A108021 A108022

Keyword

nonn,easy

Author

Alexandre Wajnberg, May 31 2005

Extensions

More terms from Robert G. Wilson v, Jun 01 2005

Status

approved