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 A120717 Expansion of -x*(378*x^3+287*x^2-134*x-67) / ((2*x+1)*(3*x-1)*(10*x^2+5*x-1)). 1
 0, 67, 536, 3666, 24834, 163870, 1077594, 7054814, 46137578, 301492462, 1969619930, 12865344702, 84029934282, 548824052494, 3584482608186, 23410842173150, 152899603572266, 998608137861166, 6522041823044762 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Old name was: Sequence produced by Markov chain based on body-centered pentagonal prism 11 X 11 bond graph. Characteristic polynomial = -480x^4 - 1040 x^5 - 752 x^6 - 120 x^7 + 90 x^8 + 35x^9- x^11. The molecule with this structure is known as Ferrocene. LINKS Dr Karl Harrison, Ferrocene, What is Ferrocene? About its Science, Chemistry and Structure Wikipedia, Ferrocene Index entries for linear recurrences with constant coefficients, signature (6,11,-40,-60). FORMULA G.f.: -x*(378*x^3+287*x^2-134*x-67) / ((2*x+1)*(3*x-1)*(10*x^2+5*x-1)). [Colin Barker, Nov 29 2012] MATHEMATICA 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] a = Table[v[n][[1]], {n, 1, 50}] CROSSREFS Sequence in context: A219736 A257747 A163150 * A200963 A245878 A142139 Adjacent sequences:  A120714 A120715 A120716 * A120718 A120719 A120720 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Aug 12 2006 EXTENSIONS Edited by N. J. A. Sloane, Jul 13 2007 New name (using g.f. by Colin Barker) by Joerg Arndt, Jan 07 2013 STATUS approved

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