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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A111384.

Programs

Magma

R:=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

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 *)

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. = PowerSeriesRing(ZZ, prec)
    return P( f(x) ).list()
A120715_list(50) # G. C. Greubel, Jul 22 2023

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

Extensions

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