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}.

2, 4, 8, 13, 21, 39, 64, 138, 236, 551, 963, 2315, 4078, 9892, 17468, 42481, 75069, 182691, 322900, 785970, 1389248, 3381731, 5977491, 14550695, 25719658, 62608228, 110665760, 269388997, 476169765, 1159120239, 2048851480

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-8,8,3,-3).

Formula

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}]

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]

Mathematica

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}]

Crossrefs

Sequence in context: A164419 A164431 A164480 * A351620 A078157 A144119

Adjacent sequences: A134032 A134033 A134034 * A134036 A134037 A134038

Keyword

nonn,uned

Author

Roger L. Bagula, Jan 11 2008

Status

approved