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 A093134 #26 Aug 21 2024 14:31:04
%S A093134 1,0,8,56,456,3640,29128,233016,1864136,14913080,119304648,954437176,
%T A093134 7635497416,61083979320,488671834568,3909374676536,31274997412296,
%U A093134 250199979298360,2001599834386888,16012798675095096,128102389400760776,1024819115206086200,8198552921648689608
%N A093134 A Jacobsthal trisection.
%C A093134 Counts closed walks at a vertex of the complete graph on 9 nodes K_9.
%C A093134 Second binomial transform is A047855.
%H A093134 Vincenzo Librandi, <a href="/A093134/b093134.txt">Table of n, a(n) for n = 0..1000</a>
%H A093134 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,8).
%F A093134 G.f.: (1-7*x)/(1 - 7*x - 8*x^2).
%F A093134 a(n) = (8^n + 8*(-1)^n)/9.
%F A093134 a(n) = 8*A001045(3*n-3)/3.
%F A093134 From _Elmo R. Oliveira_, Aug 17 2024: (Start)
%F A093134 E.g.f.: exp(-x)*(exp(9*x) + 8)/9.
%F A093134 a(n) = 7*a(n-1) + 8*a(n-2) for n > 1. (End)
%t A093134 k=0;lst={1, k};Do[k=8^n-k;AppendTo[lst, k], {n, 1, 5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008 *)
%t A093134 Table[(8^n + 8*(-1)^n)/9, {n,0,30}] (* or *) LinearRecurrence[{7,8}, {1,0}, 30] (* _G. C. Greubel_, Jan 06 2018 *)
%o A093134 (Magma) [(8^n/9+8*(-1)^n/9): n in [0..20]]; // _Vincenzo Librandi_, Oct 11 2011
%o A093134 (PARI) for(n=0,30, print1((8^n + 8*(-1)^n)/9, ", ")) \\ _G. C. Greubel_, Jan 06 2018
%Y A093134 Other sequences with a(n+1) = 8^n - a(n) are A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A015565. - _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008
%Y A093134 Cf. A047855.
%K A093134 easy,nonn
%O A093134 0,3
%A A093134 _Paul Barry_, Mar 23 2004