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A158609
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A sequence from a vector Markov with the matrix:t=3;M={{0,t},{t,1/t}} and characteristic polynomial :x^2-x/t-t^2.
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2
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1, 9, 90, 819, 8109, 74448, 731277, 6761565, 65995002, 613681767, 5959276929, 55667500056, 538368931305, 5047436435841, 48655319871546, 457497671174667, 4398578580769893, 41455889945917920, 397740754988279253
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Quadratic equation associated with group [3,3,5]
which instead of t=phi uses Integer t.
Phi(t)=(1+Sqrt[1+4*t^4])/(2*t);
t=1:Phi(1)=(1+Sqrt[5])/2;
t=2:Phi(2)=(1 + Sqrt[65])/4;
t=3:Phi(3)=(1+5*Sqrt[13))/6
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REFERENCES
| H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973,page 221.
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FORMULA
| t=3;M={{0,t},{t,1/t}};
and characteristic polynomial :x^2-x/t-t^2;
v(0)={1,1);v(n)=M.v(n-1);
out_(n)=t^n*v(n)[[1]]
a(n)=a(n-1)+81*a(n-2), a(0)=1, a(1)=9 . G.f.: (1+8x)/(1-x-81*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 26 2009]
a(n)=(1/2)*{[(1/2)-(5/2)*sqrt(13)]^n+[(1/2)+(5/2)*sqrt(13)]^n}+(17/130)*sqrt(13)*{[(1/2)+(5/2)*sqrt(13)]^n-[(1/2)-(5/2)*sqrt(13)]^n}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Mar 30 2009]
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MATHEMATICA
| Clear[M, v, t, n];
M = {{0, t}, {t, 1/t}};
v[0] = {1, 1};
v[n_] := v[n] = M.v[n - 1];
t = 3;
a = Table[t^n*v[n][[1]], {n, 0, 30}]
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CROSSREFS
| Sequence in context: A054616 A052386 A186510 * A057092 A156577 A173480
Adjacent sequences: A158606 A158607 A158608 * A158610 A158611 A158612
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 22 2009
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