A125835 Numbers whose base-8 or octal representation is 22222222.......2.

0, 2, 18, 146, 1170, 9362, 74898, 599186, 4793490, 38347922, 306783378, 2454267026, 19634136210, 157073089682, 1256584717458, 10052677739666, 80421421917330, 643371375338642, 5146971002709138, 41175768021673106, 329406144173384850, 2635249153387078802, 21081993227096630418

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 2*(8^(n-1) - 1)/7.

a(n) = 8*a(n-1) + 2, with a(1)=0. - Vincenzo Librandi, Sep 30 2010

From G. C. Greubel, Aug 03 2019: (Start)

a(n) = 2*A023001(n).

G.f.: 2*x^2/((1-x)*(1-8*x)).

E.g.f.: 2*(exp(8*x) - exp(x))/7. (End)

Example

Octal.............decimal
0.......................0
2.......................2
22.....................18
222...................146
2222.................1170
22222................9362
222222..............74898
2222222............599186
22222222..........4793490
222222222........38347922
2222222222......306783378
etc. ...............etc.

Maple

seq(2*(8^n-1)/7, n=0..30);

Mathematica

nxt2[n_]:=Module[{idn=IntegerDigits[n, 8]}, FromDigits[PadLeft[idn, Length[idn]+1, 2], 8]]; Join[{0}, NestList[nxt2, 2, 30]]  (* Harvey P. Dale, Mar 09 2011 *)
Module[{nn=30, c}, c=PadRight[{}, nn, 2]; Table[FromDigits[Take[c, n], 8], {n, 0, nn}]] (* Harvey P. Dale, Sep 05 2015 *)
2*(8^(Range[30]-1) -1)/7 (* G. C. Greubel, Aug 03 2019 *)

Prog

(PARI) a(n)=2*(1<<(3*n-3)\7) \\ Charles R Greathouse IV, Mar 09 2011
(PARI) vector(30, n, 2*(8^(n-1) -1)/7) \\ G. C. Greubel, Aug 03 2019
(Magma) [2*(8^(n-1) -1)/7: n in [1..30]]; // G. C. Greubel, Aug 03 2019
(Sage) [2*(8^(n-1) -1)/7 for n in (1..30)] # G. C. Greubel, Aug 03 2019
(GAP) List([1..30], n-> 2*(8^(n-1) -1)/7); # G. C. Greubel, Aug 03 2019

Crossrefs

Cf. A023001.

Sequence in context: A208654 A037565 A329170 * A356623 A091170 A207319

Adjacent sequences: A125832 A125833 A125834 * A125836 A125837 A125838

Keyword

easy,nonn

Author

Zerinvary Lajos, Feb 03 2007

Extensions

Offset corrected by N. J. A. Sloane, Oct 02 2010

Terms a(21) onward added by G. C. Greubel, Aug 03 2019

Status

approved