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

Author

Alexandre Wajnberg, May 31 2005

Keywords

• nonn
• easy

Comments

Numbers n whose binary representation is 100, n times.

Examples

			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)
		

Links

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

Crossrefs

Cf. A020988.

Programs

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 *)

PARI

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

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)

Extensions

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