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A024088 a(n) = 8^n - 1.

%I A024088 #34 Sep 08 2022 08:44:48
%S A024088 0,7,63,511,4095,32767,262143,2097151,16777215,134217727,1073741823,
%T A024088 8589934591,68719476735,549755813887,4398046511103,35184372088831,
%U A024088 281474976710655,2251799813685247,18014398509481983
%N A024088 a(n) = 8^n - 1.
%C A024088 Numbers whose base 8 or octal representation is 777777.......7. - _Zerinvary Lajos_, Feb 03 2007
%H A024088 G. C. Greubel, <a href="/A024088/b024088.txt">Table of n, a(n) for n = 0..1000</a>
%H A024088 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F A024088 From _Mohammad K. Azarian_, Jan 14 2009: (Start)
%F A024088 G.f.: 1/(1-8*x) - 1/(1-x).
%F A024088 E.g.f.: exp(8*x) - exp(x). (End)
%F A024088 a(n) = A000225(n)*A001576(n). - _Reinhard Zumkeller_, Feb 15 2009
%F A024088 a(n) = 8*a(n-1) + 7 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A024088 a(n) = Sum_{i=1..n} 7^i*binomial(n,n-i) for n>0, a(0)=0. - _Bruno Berselli_, Nov 11 2015
%F A024088 a(n) = A001018(n) - 1. - _Sean A. Irvine_, Jun 19 2019
%F A024088 Sum_{n>=1} 1/a(n) = A248725. - _Amiram Eldar_, Nov 13 2020
%t A024088 8^Range[0,20]-1 (* or *) LinearRecurrence[{9,-8},{0,7},20] (* _Harvey P. Dale_, Jan 04 2017 *)
%o A024088 (Sage) [gaussian_binomial(3*n,1,2) for n in range(0,20)] # _Zerinvary Lajos_, May 28 2009
%o A024088 (Sage) [stirling_number2(3*n+1,2) for n in range(0,20)] # _Zerinvary Lajos_, Nov 26 2009
%o A024088 (Sage) [8^n-1 for n in (0..20)] # _Bruno Berselli_, Nov 11 2015
%o A024088 (PARI) vector(20, n, n--; 8^n -1) \\ _G. C. Greubel_, Aug 03 2019
%o A024088 (Magma) [8^n -1: n in [0..20]]; // _G. C. Greubel_, Aug 03 2019
%o A024088 (GAP) List([0..30], n-> 8^n -1); # _G. C. Greubel_, Aug 03 2019
%Y A024088 Cf. A000225, A001576, A001018, A248725.
%K A024088 nonn,easy
%O A024088 0,2
%A A024088 _N. J. A. Sloane_