A107451 Let m = 5 and set M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, m, (m + 1), -m*(m + 1), -m, (m + 2)}}. Let v[0] = {0, 1, 1, 2, 3, 5}, v[n] = M.v[n - 1]. Then a = Abs[v[n][[1]].

1, 1, 2, 3, 5, 29, 302, 2092, 12221, 66179, 341350, 1705958, 8333070, 40017287, 189643693, 889303635, 4134575230, 19086260759, 87581455636, 399845651745, 1817488787127, 8230050719153, 37144327008467, 167153266777585

Offset

0,3

Comments

Based on a Markov chain with characteristic polynomial 1 - m* x - (m + 1) *x^2 + m*(m + 1)* x^3 + m* x^4 - (m + 2)* x^5 + x^6 with m=5.

This is a doubled Bombieri polynomial with real roots {{x -> -1.64378}, {x -> -0.425321}, {x -> 0.201585}, {x -> 0.395849}, {x -> 4.10318}, {x -> 4.36848}}. The base vector is Fibonacci-like.

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (7,-5,-30,6,5,-1).

Formula

G.f.: (10*x^10-44*x^9-86*x^8+246*x^7+198*x^6+58*x^5+18*x^4+24*x^3-6*x+1) / (x^6-5*x^5-6*x^4+30*x^3+5*x^2-7*x+1). - Colin Barker, May 17 2013

Mathematica

M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, m, (m + 1), -m*(m + 1), -m, (m + 2)}} Det[M - x*IdentityMatrix[6]] m = 5; NSolve[Det[M - x*IdentityMatrix[6]] == 0, x] v[0] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}]

Crossrefs

Sequence in context: A062167 A358896 A279189 * A093490 A073309 A226124

Adjacent sequences: A107448 A107449 A107450 * A107452 A107453 A107454

Keyword

nonn,easy

Author

Roger L. Bagula, May 26 2005

Extensions

Edited by N. J. A. Sloane, Jun 16 2007

Status

approved