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A107378 Expansion of x*(1-3*x-2*x^2)/(1-4*x+4*x^3+x^4). 1
0, 1, 1, 2, 4, 11, 35, 122, 440, 1609, 5913, 21770, 80204, 295555, 1089227, 4014322, 14794864, 54526993, 200961457, 740652050, 2729705364, 10060448635, 37078224883, 136653426026, 503642204200, 1856195468633, 6841089945545 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..26.

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

Cf. A107377.

Sequence in context: A234006 A285002 A340338 * A186998 A243788 A245465

Adjacent sequences:  A107375 A107376 A107377 * A107379 A107380 A107381

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, May 24 2005

EXTENSIONS

Edited by N. J. A. Sloane, Jul 13 2007

STATUS

approved

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Last modified June 16 18:25 EDT 2021. Contains 345066 sequences. (Running on oeis4.)