OFFSET
0,4
COMMENTS
Sequence produced by 4 X 4 Markov chain with characteristic polynomial x^4-4*x^3+4*x+1.
Setting m=3 gives a Fibonacci sequence.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,0,-4,-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]]] NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1]; digits = 50; a = Table[v[n][[1]], {n, 1, digits}]
CoefficientList[Series[x (1-3x-2x^2)/(1-4x+4x^3+x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 0, -4, -1}, {0, 1, 1, 2}, 30] (* Harvey P. Dale, Aug 30 2020 *)
PROG
(PARI) Vec(x*(1-3*x-2*x^2)/(1-4*x+4*x^3+x^4)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, May 24 2005
EXTENSIONS
Edited by N. J. A. Sloane, Jul 13 2007
STATUS
approved