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A134035 The 4 X 4 Fibonacci/ anti-Fibonacci game switched modulo 2 with its dual: MA1={{0,1},{1,1}};MB1={{0,1}{1,3}}; MA2={{0,1},1,3}};MB2={{1,0},{1,1}}; the game has two characteristic polynomials: (-3 + 5 x - 3 x^3 + x^4, -1 + x + 2 x^2 - 3 x^3 + x^4}. 0

%I

%S 2,4,8,13,21,39,64,138,236,551,963,2315,4078,9892,17468,42481,75069,

%T 182691,322900,785970,1389248,3381731,5977491,14550695,25719658,

%U 62608228,110665760,269388997,476169765,1159120239,2048851480

%N The 4 X 4 Fibonacci/ anti-Fibonacci game switched modulo 2 with its dual: MA1={{0,1},{1,1}};MB1={{0,1}{1,3}}; MA2={{0,1},1,3}};MB2={{1,0},{1,1}}; the game has two characteristic polynomials: (-3 + 5 x - 3 x^3 + x^4, -1 + x + 2 x^2 - 3 x^3 + x^4}.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-8,8,3,-3).

%F M[n_] := If[Mod[n,2] == 1, {{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 3, 1}}, {{0, 1, 0, 0}, {3, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 1, 1}}]; v[1] = {0, 1, 1, 0}; v[n_] := v[n] = M[n].v[n - 1] a(n) =Sum[v[n][[i]],{i,1,4}]

%F a(n) = +a(n-1) +6*a(n-2) -6*a(n-3) -8*a(n-4) +8*a(n-5) +3*a(n-6) -3*a(n-7). G.f.: x*(2+2*x-8*x^2-7*x^3+4*x^5+3*x^6) / ( (1+x)*(3*x^4-5*x^2+1)*(x-1)^2 ). [From _R. J. Mathar_, May 24 2010]

%t M[n_] := If[Mod[n,2] == 1, {{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 3, 1}}, {{0, 1, 0, 0}, {3, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 1, 1}}]; v[1] = {0, 1, 1, 0}; v[n_] := v[n] = M[n].v[n - 1]; a = Table[Apply[Plus, v[n]], {n, 1, 50}] Table[Det[M[n] - x*IdentityMatrix[4]], {n, 0, 1}]

%K nonn,uned

%O 1,1

%A _Roger L. Bagula_, Jan 11 2008

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)