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 A120717 #25 Jul 21 2023 04:23:16
%S A120717 0,67,536,3666,24834,163870,1077594,7054814,46137578,301492462,
%T A120717 1969619930,12865344702,84029934282,548824052494,3584482608186,
%U A120717 23410842173150,152899603572266,998608137861166,6522041823044762
%N A120717 Expansion of x*(67 + 134*x - 287*x^2 - 378*x^3)/((1+2*x)*(1-3*x)*(1 - 5*x - 10*x^2)).
%C A120717 Old name was: Sequence produced by Markov chain based on body-centered pentagonal prism 11 X 11 bond graph.
%C A120717 Characteristic polynomial = -480*x^4 - 1040*x^5 - 752*x^6 - 120*x^7 + 90*x^8 + 35*x^9 - x^11.
%C A120717 The molecule with this structure is known as Ferrocene.
%H A120717 G. C. Greubel, <a href="/A120717/b120717.txt">Table of n, a(n) for n = 0..1000</a>
%H A120717 Dr Karl Harrison, <a href="http://www.3dchem.com/molecules.asp?ID=33">Ferrocene, What is Ferrocene? About its Science, Chemistry and Structure</a>
%H A120717 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ferrocene">Ferrocene</a>
%H A120717 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,11,-40,-60).
%F A120717 G.f.: x*(67 + 134*x - 287*x^2 - 378*x^3)/((1+2*x)*(1-3*x)*(1 - 5*x - 10*x^2)). - _Colin Barker_, Nov 29 2012
%F A120717 a(n) = (1/10)*(-63*[n=0] + 49*(-2)^n - 74*3^n + 22*(4*A180250(n) + 25*A180250(n-1))). - _G. C. Greubel_, Jul 21 2023
%t A120717 M0 = {{0,1,1,1,1,1,0,0,0,0,1}, {1,0,1,1,1,0,1,0,0,0,1}, {1,1,0,1,1,0, 0,1,0,0,1}, {1,1,1,0,1,0,0,0,1,0,1}, {1,1,1,1,0,0,0,0,0,1,1}, {1,0, 0,0,0,0,1,1,1,1,1}, {0,1,0,0,0,1,0,1,1,1,1}, {0,0,1,0,0,1,1,0,1,1, 1}, {0,0,0,1,0,1,1,1,0,1,1}, {0,0,0,0,1,1,1,1,1,0,1}, {1,1,1,1,1,1, 1,1,1,1,0}}; v[1]= Table[Fibonacci[n], {n,0,10}]; v[n_]:= v[n] = M0.v[n-1]; Table[v[n][[1]], {n,50}]
%t A120717 LinearRecurrence[{6,11,-40,-60},{0,67,536,3666,24834},20] (* _Harvey P. Dale_, May 25 2023 *)
%o A120717 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( x*(67+134*x-287*x^2-378*x^3)/((1+2*x)*(1-3*x)*(1-5*x-10*x^2)) )); // _G. C. Greubel_, Jul 21 2023
%o A120717 (SageMath)
%o A120717 A180250= BinaryRecurrenceSequence(5,10,0,1)
%o A120717 def A120717(n): return (1/10)*(-63*int(n==0) + 49*(-2)^n - 74*3^n + 22*(4*A180250(n+1) + 25*A180250(n)))
%o A120717 [A120717(n) for n in range(41)] # _G. C. Greubel_, Jul 21 2023
%Y A120717 Cf. A180250.
%K A120717 nonn,easy
%O A120717 0,2
%A A120717 _Roger L. Bagula_, Aug 12 2006
%E A120717 Edited by _N. J. A. Sloane_, Jul 13 2007
%E A120717 New name (using g.f. by _Colin Barker_) by _Joerg Arndt_, Jan 07 2013