|
Search: id:A107388
|
|
|
| A107388 |
|
A quartic Fibonacci type alternating / chaotic vector Markov sequence of a quartic characteristic:x^4+4*x^2-4*x-1. |
|
+0
1
|
|
| 0, 1, 1, 2, 1, 1, 4, 7, 7, 2, 9, 23, 32, 25, 7, 62, 119, 137, 68, 113, 369, 574, 529, 47, 896, 1999, 2575, 1726, 1169, 5743, 10044, 10601, 3689, 12098, 32743, 47033, 38624, 6217, 85993, 171650, 204057, 111847, 145796, 521503, 837407, 803458, 136159, 1222751
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Real roots: {{x -> -3.73205}, {x -> -1.}, {x -> -0.267949}, {x -> 1.}}
|
|
FORMULA
|
m=4 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, -m}}; v[n] = M.v[n - 1] a(n) =Abs[v[n][[1]]]
|
|
MATHEMATICA
|
m = 4 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, - m) Expand[Det[M - x*IdentityMatrix[4]]] (*-1 - 4 x + 4 x^3 + x^4*) NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M . v[n - 1] digits = 50; aa = Table[Abs[v[n][[1]], {n, 1, digits}]
|
|
CROSSREFS
|
Sequence in context: A096540 A107386 A107387 this_sequence A107389 A111569 A055130
Adjacent sequences: A107385 A107386 A107387 this_sequence A107389 A107390 A107391
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 24 2005
|
|
|
Search completed in 0.002 seconds
|
