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, 1, 1, 2, 31, 80, 690, 2522, 16463, 71361, 410068, 1933079, 10454444, 51354986, 269730280, 1351952533, 7000832157, 35436588070, 182241654663, 926897102096, 4750855253550, 24219753328074, 123937215821147, 632547978692149

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