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.

0, 27, 838, 4025, 29742, 161630, 962784, 5335471, 30120946, 166834881, 926998480, 5122817760, 28316610392, 156260679433, 862162027134, 4754345230927, 26214240435218, 144511100239056, 796592187757696

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

G. C. Greubel, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Fano Plane

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

Formula

G.f.: x*(27 +784*x +1539*x^2 -3286*x^3 -6475*x^4 -1442*x^5 -3783*x^6 -4444*x^7 -986*x^8)/((1 -x -x^2)*(1 +3*x +x^2)*(1 -5*x -3*x^2 +x^3)*(1 +x -11*x^2 -17*x^3)). - 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];
Table[v[n][[1]], {n, 50}]
LinearRecurrence[{2, 30, -6, -263, -250, 419, 666, 228, -28, -17}, {0, 27, 838, 4025, 29742, 161630, 962784, 5335471, 30120946, 166834881}, 50] (* G. C. Greubel, Jul 22 2023 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x*(27+784*x+1539*x^2-3286*x^3-6475*x^4-1442*x^5-3783*x^6-4444*x^7 -986*x^8)/((1-x-x^2)*(1+3*x+x^2)*(1-5*x-3*x^2+x^3)*(1+x-11*x^2 -17*x^3)) )); // G. C. Greubel, Jul 22 2023
(SageMath)
def f(x): return x*(27+784*x+1539*x^2-3286*x^3-6475*x^4-1442*x^5-3783*x^6-4444*x^7 -986*x^8)/((1-x-x^2)*(1+3*x+x^2)*(1-5*x-3*x^2+x^3)*(1+x-11*x^2 -17*x^3))
def A120715_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(x) ).list()
A120715_list(50) # G. C. Greubel, Jul 22 2023

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 L. Bagula, Aug 12 2006, corrected Jul 14 2007

Extensions

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

Status

approved