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 A190975 #49 Sep 08 2022 08:45:57 %S A190975 0,1,8,62,480,3716,28768,222712,1724160,13347856,103334528,799980512, %T A190975 6193175040,47945439296,371177164288,2873526435712,22245857157120, %U A190975 172219804385536,1333266720770048,10321694157389312,79907019817574400,618612770225816576 %N A190975 a(n) = 8*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1. %C A190975 a(n+1) equals the number of words of length n over {0,1,2,3,4,5,6,7} avoiding 01 and 02. - _Milan Janjic_, Dec 17 2015 %H A190975 G. C. Greubel, <a href="/A190975/b190975.txt">Table of n, a(n) for n = 0..1000</a> %H A190975 Tomislav Doslic, <a href="http://dx.doi.org/10.1007/s10910-013-0167-2">Planar polycyclic graphs and their Tutte polynomials</a>, Journal of Mathematical Chemistry, Volume 51, Issue 6, 2013, pp. 1599-1607. See Cor. 3.7(e). %H A190975 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -2). %F A190975 a(n) = ((4 + sqrt(14))^n - (4 - sqrt(14))^n)/(2*sqrt(14)). - _Giorgio Balzarotti_, May 28 2011 %F A190975 G.f.: x/(1 - 8x + 2*x^2). - _Philippe Deléham_, Oct 12 2011 %F A190975 E.g.f.: (1/sqrt(14))*exp(4*x)*sinh(sqrt(14)*x). - _G. C. Greubel_, Dec 18 2015 %t A190975 LinearRecurrence[{8,-2}, {0,1}, 50] %o A190975 (Magma) I:=[0,1]; [n le 2 select I[n] else 8*Self(n-1)-2*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Dec 17 2015 %o A190975 (PARI) Vec(1/(1-8*x+2*x^2) + O(x^100)) \\ _Altug Alkan_, Dec 17 2015 %Y A190975 Cf. A190958 (index to generalized Fibonacci sequences). %K A190975 nonn %O A190975 0,3 %A A190975 _Vladimir Joseph Stephan Orlovsky_, May 24 2011