This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139634 #45 Dec 29 2023 10:08:56
%S A139634 1,11,31,71,151,311,631,1271,2551,5111,10231,20471,40951,81911,163831,
%T A139634 327671,655351,1310711,2621431,5242871,10485751,20971511,41943031,
%U A139634 83886071,167772151,335544311,671088631,1342177271,2684354551
%N A139634 a(n) = 10*2^(n-1) - 9.
%C A139634 Binomial transform of [1, 10, 10, 10,...].
%C A139634 A007318 * [1, 10, 10, 10,...].
%C A139634 The binomial transform of [1, c, c, c,...] has the terms a(n)=1-c+c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c-2)x}/{(2x-1)(x-1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - _R. J. Mathar_, May 11 2008
%H A139634 Vincenzo Librandi, <a href="/A139634/b139634.txt">Table of n, a(n) for n = 1..1000</a>
%H A139634 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A139634 a(n) = 2*a(n-1) + 9, with n>1, a(1)=1. - _Vincenzo Librandi_, Nov 24 2010
%F A139634 From _Colin Barker_, Oct 10 2013: (Start)
%F A139634 a(n) = 3*a(n-1) - 2*a(n-2).
%F A139634 G.f.: x*(8*x+1) / ((x-1)*(2*x-1)). (End)
%e A139634 a(4) = 71 = (1, 3, 3, 1) dot (1, 10, 10, 10) = (1 + 30 + 30 + 10).
%p A139634 A139634:=n->10*2^(n-1)-9; seq(A139634(n), n=1..30); # _Wesley Ivan Hurt_, Mar 26 2014
%t A139634 a=1; lst={a}; k=10; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008 *)
%t A139634 CoefficientList[Series[(8 x + 1)/((x - 1) (2 x - 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 30 2014 *)
%t A139634 LinearRecurrence[{3,-2},{1,11},30] (* _Harvey P. Dale_, Feb 19 2023 *)
%o A139634 (Magma) [10*2^(n-1)-9: n in [1..50]]; // _Vincenzo Librandi_, Mar 30 2014
%o A139634 (PARI) a(n)=10*2^(n-1)-9 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A139634 Cf. A007318.
%K A139634 nonn,easy
%O A139634 1,2
%A A139634 _Gary W. Adamson_, Apr 29 2008
%E A139634 More terms from _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008
%E A139634 Simpler definition from _Jon E. Schoenfield_, Jun 23 2010