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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.

%I A120715 #18 Feb 16 2025 08:33:02
%S A120715 0,27,838,4025,29742,161630,962784,5335471,30120946,166834881,
%T A120715 926998480,5122817760,28316610392,156260679433,862162027134,
%U A120715 4754345230927,26214240435218,144511100239056,796592187757696
%N 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.
%C A120715 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.
%H A120715 G. C. Greubel, <a href="/A120715/b120715.txt">Table of n, a(n) for n = 0..1000</a>
%H A120715 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FanoPlane.html">Fano Plane</a>
%H A120715 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,30,-6,-263,-250,419,666,228,-28,-17).
%F A120715 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
%t A120715 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}};
%t A120715 v[1]= Table[Fibonacci[n], {n,0,13}]; v[n_]:= v[n]= M.v[n-1];
%t A120715 Table[v[n][[1]], {n,50}]
%t A120715 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 *)
%o A120715 (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
%o A120715 (SageMath)
%o A120715 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))
%o A120715 def A120715_list(prec):
%o A120715     P.<x> = PowerSeriesRing(ZZ, prec)
%o A120715     return P( f(x) ).list()
%o A120715 A120715_list(50) # _G. C. Greubel_, Jul 22 2023
%Y A120715 Cf. A111384.
%K A120715 nonn,easy
%O A120715 0,2
%A A120715 _Roger L. Bagula_, Aug 12 2006, corrected Jul 14 2007
%E A120715 Edited by _N. J. A. Sloane_, Jul 14 2007