|
Search: id:A158608
|
|
|
| A158608 |
|
A sequence from a vector Markov with the matrix:t=2;M={{0,t},{t,1/t}} and characteristic polynomial :x^2-x/t-t^2. |
|
+0
4
|
|
| 1, 4, 20, 84, 404, 1748, 8212, 36180, 167572, 746452, 3427604, 15370836, 70212500, 316145876, 1439545876, 6497879892, 29530613908, 133496692180, 605986514708, 2741933589588, 12437717824916, 56308655258324, 255312140456980
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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
|
|
REFERENCES
|
H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973,page 221.
|
|
FORMULA
|
t=2;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)+16*a(n-2), a(0)=1, a(1)=4. G.f.: (1+3x)/(1-x-16*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 26 2009]
a(n)=(1/2)*{[(1/2)-(1/2)*sqrt(65)]^n+[(1/2)+(1/2)*sqrt(65)]^n}+(7/130)*sqrt(65)*{[(1/2)+(1/2)*sqrt(65)]^n-[(1/2)-(1/2)*sqrt(65)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Mar 30 2009]
|
|
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 = 2;
a = Table[t^n*v[n][[1]], {n, 0, 30}]
|
|
CROSSREFS
|
Sequence in context: A084240 A080674 A110154 this_sequence A093357 A027156 A017964
Adjacent sequences: A158605 A158606 A158607 this_sequence A158609 A158610 A158611
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 22 2009
|
|
|
Search completed in 0.002 seconds
|
