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A120715 Sequence produced by 14 X 14 Markov chain based on 14-vertex graph formed from direct product of two copies of the graph used in A120714. 1
0, 27, 838, 4025, 29742, 161630, 962784, 5335471, 30120946, 166834881, 926998480, 5122817760, 28316610392, 156260679433, 862162027134, 4754345230927, 26214240435218, 144511100239056, 796592187757696 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Characteristic polynomial : -17 - 96 x + 65 x^2 + 1528 x^3 + 3840 x^4 + 2996 x^5 - 1566 x^6 - 3312 x^7 - 702 x^8 + 880 x^9 + 372 x^10 - 52 x^11 - 37 x^12 + x^14.

LINKS

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

Eric Weisstein's World of Mathematics, Fano Plane

Index to sequences with linear recurrences with constant coefficients, signature (2,30,-6,-263,-250,419,666,228,-28,-17).

FORMULA

G.f.: -x*(986*x^8+4444*x^7+3783*x^6+1442*x^5+6475*x^4+3286*x^3-1539*x^2-784*x-27) / ((x^2+x-1)*(x^2+3*x+1)*(x^3-3*x^2-5*x+1)*(17*x^3+11*x^2-x-1)). [Colin Barker, Nov 29 2012]

MATHEMATICA

M = {{0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0}, {1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0}, {0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0}, {0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0}, {1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1}, {0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1}, {0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 13}] v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]

CROSSREFS

Cf. A111384.

Sequence in context: A183505 A218717 A159234 * A065922 A061695 A107050

Adjacent sequences:  A120712 A120713 A120714 * A120716 A120717 A120718

KEYWORD

nonn,easy

AUTHOR

Roger Bagula, Aug 12 2006, corrected Jul 14 2007

EXTENSIONS

Edited by N. J. A. Sloane, Jul 14 2007

STATUS

approved

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Last modified May 20 15:50 EDT 2013. Contains 225463 sequences.