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A104095 Let v[0]={0,1,1,2}, v[n]=M.v[n-1], where M={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 10, 19, 1}}; then a(n) =v[n][[1]] (the first term). 0
0, 1, 1, 2, 31, 80, 690, 2522, 16463, 71361, 410068, 1933079, 10454444, 51354986, 269730280, 1351952533, 7000832157, 35436588070, 182241654663, 926897102096, 4750855253550, 24219753328074, 123937215821147, 632547978692149 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1, 19, 10, 1).

FORMULA

G.f.: (-18*x^3 + x)/(-x^4 - 10*x^3 - 19*x^2 - x + 1).

a(0)=0, a(1)=a(2)=1, a(3)=2, a(n)=a(n-1)+19a(n-2)+10a(n-3)+a(n-4) [From Harvey P. Dale, Apr 26 2011]

MATHEMATICA

M={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 10, 19, 1}} v[0] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 0, 50}]

LinearRecurrence[{1, 19, 10, 1}, {0, 1, 1, 2}, 40] (* or *) CoefficientList[ Series[(-18x^3+x)/(-x^4-10x^3-19x^2-x+1), {x, 0, 40}], x]  (* Harvey P. Dale, Apr 26 2011 *)

CROSSREFS

Sequence in context: A302361 A175446 A054207 * A282725 A030459 A141978

Adjacent sequences:  A104092 A104093 A104094 * A104096 A104097 A104098

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Mar 31 2005

STATUS

approved

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Last modified June 16 04:56 EDT 2021. Contains 345056 sequences. (Running on oeis4.)