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

%I A125835 #38 Mar 01 2022 20:34:28
%S A125835 0,2,18,146,1170,9362,74898,599186,4793490,38347922,306783378,
%T A125835 2454267026,19634136210,157073089682,1256584717458,10052677739666,
%U A125835 80421421917330,643371375338642,5146971002709138,41175768021673106,329406144173384850,2635249153387078802,21081993227096630418
%N A125835 Numbers whose base-8 or octal representation is 22222222.......2.
%H A125835 G. C. Greubel, <a href="/A125835/b125835.txt">Table of n, a(n) for n = 1..1000</a>
%H A125835 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F A125835 a(n) = 2*(8^(n-1) - 1)/7.
%F A125835 a(n) = 8*a(n-1) + 2, with a(1)=0. - _Vincenzo Librandi_, Sep 30 2010
%F A125835 From _G. C. Greubel_, Aug 03 2019: (Start)
%F A125835 a(n) = 2*A023001(n).
%F A125835 G.f.: 2*x^2/((1-x)*(1-8*x)).
%F A125835 E.g.f.: 2*(exp(8*x) - exp(x))/7. (End)
%e A125835 Octal.............decimal
%e A125835 0.......................0
%e A125835 2.......................2
%e A125835 22.....................18
%e A125835 222...................146
%e A125835 2222.................1170
%e A125835 22222................9362
%e A125835 222222..............74898
%e A125835 2222222............599186
%e A125835 22222222..........4793490
%e A125835 222222222........38347922
%e A125835 2222222222......306783378
%e A125835 etc. ...............etc.
%p A125835 seq(2*(8^n-1)/7, n=0..30);
%t A125835 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 *)
%t A125835 Module[{nn=30,c},c=PadRight[{},nn,2];Table[FromDigits[Take[c,n],8],{n,0,nn}]] (* _Harvey P. Dale_, Sep 05 2015 *)
%t A125835 2*(8^(Range[30]-1) -1)/7 (* _G. C. Greubel_, Aug 03 2019 *)
%o A125835 (PARI) a(n)=2*(1<<(3*n-3)\7) \\ _Charles R Greathouse IV_, Mar 09 2011
%o A125835 (PARI) vector(30, n, 2*(8^(n-1) -1)/7) \\ _G. C. Greubel_, Aug 03 2019
%o A125835 (Magma) [2*(8^(n-1) -1)/7: n in [1..30]]; // _G. C. Greubel_, Aug 03 2019
%o A125835 (Sage) [2*(8^(n-1) -1)/7 for n in (1..30)] # _G. C. Greubel_, Aug 03 2019
%o A125835 (GAP) List([1..30], n-> 2*(8^(n-1) -1)/7); # _G. C. Greubel_, Aug 03 2019
%Y A125835 Cf. A023001.
%K A125835 easy,nonn
%O A125835 1,2
%A A125835 _Zerinvary Lajos_, Feb 03 2007
%E A125835 Offset corrected by _N. J. A. Sloane_, Oct 02 2010
%E A125835 Terms a(21) onward added by _G. C. Greubel_, Aug 03 2019