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 A139635 #33 Sep 27 2024 05:22:04
%S A139635 1,12,34,78,166,342,694,1398,2806,5622,11254,22518,45046,90102,180214,
%T A139635 360438,720886,1441782,2883574,5767158,11534326,23068662,46137334,
%U A139635 92274678,184549366,369098742,738197494,1476394998,2952790006,5905580022,11811160054
%N A139635 Binomial transform of [1, 11, 11, 11, ...].
%C A139635 A007318 * [1, 11, 11, 11, ...].
%C A139635 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 A139635 Vincenzo Librandi, <a href="/A139635/b139635.txt">Table of n, a(n) for n = 1..1000</a>
%H A139635 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A139635 a(n) = 11*2^(n-1) - 10. - _Emeric Deutsch_, May 03 2008
%F A139635 a(n) = 2*a(n-1) + 10, with n > 1, a(1)=1. - _Vincenzo Librandi_, Nov 24 2010
%F A139635 From _Colin Barker_, Mar 11 2014: (Start)
%F A139635 a(n) = 3*a(n-1) - 2*a(n-2).
%F A139635 G.f.: x*(9*x+1) / ((x-1)*(2*x-1)). (End)
%e A139635 a(4) = 78 = (1, 3, 3, 1) dot (1, 11, 11, 11) = (1 + 33 + 33 + 11).
%p A139635 seq(11*2^(n-1)-10,n=1.. 25); # _Emeric Deutsch_, May 03 2008
%t A139635 a=1; lst={a}; k=11; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008 *)
%t A139635 CoefficientList[Series[(9 x + 1)/((x - 1) (2 x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 13 2014 *)
%t A139635 LinearRecurrence[{3,-2},{1,12},40] (* _Harvey P. Dale_, Oct 26 2015 *)
%o A139635 (PARI) Vec(x*(9*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 11 2014
%Y A139635 Cf. A139634.
%K A139635 nonn,easy
%O A139635 1,2
%A A139635 _Gary W. Adamson_, Apr 29 2008
%E A139635 More terms from _Emeric Deutsch_, May 03 2008
%E A139635 More terms from _Colin Barker_, Mar 11 2014