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 A187709 #54 Jan 28 2025 08:01:14
%S A187709 1,8,71,638,5741,51668,465011,4185098,37665881,338992928,3050936351,
%T A187709 27458427158,247125844421,2224132599788,20017193398091,
%U A187709 180154740582818,1621392665245361,14592533987208248,131332805884874231,1181995252963868078,10637957276674812701,95741615490073314308,861674539410659828771
%N A187709 a(n) = (7*9^n + 1)/8.
%C A187709 Case r=9 in a(n)=((r-2)*r^n+1)/(r-1).
%H A187709 G. C. Greubel, <a href="/A187709/b187709.txt">Table of n, a(n) for n = 0..1000</a>
%H A187709 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A187709 a(n) = (7*9^n + 1)/8.
%F A187709 a(n) = +10*a(n-1) -9*a(n-2).
%F A187709 a(n) = 8*Sum_{i=0..n-1} a(i) -n + 1.
%F A187709 G.f.: (1-2*x)/((1-x)*(1-9*x)).
%F A187709 a(n) = 9^n - Sum_{i=0..n-1} 9^i for n>0. - _Bruno Berselli_, Jun 20 2013
%F A187709 E.g.f.: (7*exp(9*x) + exp(x))/8. - _G. C. Greubel_, Nov 06 2018
%t A187709 (7*9^Range[0,30]+1)/8 (* or *) LinearRecurrence[{10,-9},{1,8},30] (* _Harvey P. Dale_, Jul 20 2012 *)
%o A187709 (Magma) [(7*9^n+1)/8: n in [0..25]]; // _Vincenzo Librandi_, Mar 30 2011
%o A187709 (PARI) a(n)=(7*9^n+1)/8 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A187709 Cf. A007051, A083068, A270472 (first differences), A059482: cases r=3,8,10 in ((r-2)*r^n+1)/(r-1), respectively.
%K A187709 nonn,easy
%O A187709 0,2
%A A187709 _Sture Sjöstedt_, Mar 30 2011
%E A187709 Additional formulas from _Bruno Berselli_