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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

Table of n, a(n) for n=0..18.

Dr Karl Harrison, Ferrocene, What is Ferrocene? About its Science, Chemistry and Structure

Wikipedia, Ferrocene

Index to sequences with 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: A142735 A219736 A163150 * A200963 A142139 A178004

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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Last modified April 23 19:18 EDT 2014. Contains 240946 sequences.