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 A135030 #51 Sep 08 2022 08:45:32
%S A135030 0,1,6,38,240,1516,9576,60488,382080,2413456,15244896,96296288,
%T A135030 608267520,3842197696,24269721216,153302722688,968355778560,
%U A135030 6116740116736,38637152257536,244056393778688,1541612667187200
%N A135030 Generalized Fibonacci numbers: a(n) = 6*a(n-1) + 2*a(n-2).
%C A135030 For n>0, a(n) equals the number of words of length n-1 over {0,1,...,7} in which 0 and 1 avoid runs of odd lengths. - _Milan Janjic_, Jan 08 2017
%H A135030 Joshua Zucker and Robert Israel, <a href="/A135030/b135030.txt">Table of n, a(n) for n = 0..1000</a> (n=0..51 from Joshua Zucker).
%H A135030 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, 2).
%F A135030 a(0) = 0; a(1) = 1; a(n) = 2*(3*a(n-1) + a(n-2)).
%F A135030 a(n) = 1/(2*sqrt(11))*( (3 + sqrt(11))^n - (3 - sqrt(11))^n ).
%F A135030 G.f.: x/(1 - 6*x - 2*x^2). - _Harvey P. Dale_, Jun 20 2011
%F A135030 a(n+1) = Sum_{k=0..n} A099097(n,k)*2^k. - _Philippe Deléham_, Sep 16 2014
%F A135030 E.g.f.: (1/sqrt(11))*exp(3*x)*sinh(sqrt(11)*x). - _G. C. Greubel_, Sep 17 2016
%p A135030 A:= gfun:-rectoproc({a(0) = 0, a(1) = 1, a(n) = 2*(3*a(n-1) + a(n-2))},a(n),remember):
%p A135030 seq(A(n),n=1..30); # _Robert Israel_, Sep 16 2014
%t A135030 Join[{a=0,b=1},Table[c=6*b+2*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)
%t A135030 LinearRecurrence[{6,2},{0,1},30] (* or *) CoefficientList[Series[ -(x/(2x^2+6x-1)),{x,0,30}],x] (* _Harvey P. Dale_, Jun 20 2011 *)
%o A135030 (Sage) [lucas_number1(n,6,-2) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009
%o A135030 (Magma) [n le 2 select n-1 else 6*Self(n-1) + 2*Self(n-2): n in [1..35]]; // _Vincenzo Librandi_, Sep 18 2016
%o A135030 (PARI) a(n)=([0,1; 2,6]^n*[0;1])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016
%Y A135030 Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A015548, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226, A180250.
%K A135030 nonn,easy
%O A135030 0,3
%A A135030 _Rolf Pleisch_, Feb 10 2008, Feb 14 2008
%E A135030 More terms from _Joshua Zucker_, Feb 23 2008