OFFSET
0,5
COMMENTS
Original name was: Sequence obtained using characteristic polynomial that is Laplace transform of the minimal Pisot characteristic polynomial: -s^4*L(t^3-t-1) = s^3 + s^2-6.
LINKS
Robert Israel, Table of n, a(n) for n = 0..3380
FORMULA
G.f. of b(n): (x+2*x^2)/(1+x-6*x^3). - Robert Israel, Jun 27 2018
MAPLE
f:= gfun:-rectoproc({a(n) = -a(n-1)+6*a(n-3), a(0)=0, a(1)=1, a(2)=1}, a(n), remember):
map(abs@f, [$0..50]); # Robert Israel, Jun 27 2018
MATHEMATICA
(* first method *) F[1] = 0; F[2] = 1; F[3] = 1; F[n__] := F[n] = -F[n - 1] + 6*F[n - 3] a = Table[Abs[F[n]], {n, 1, 50}] (*second method*) M = {{0, 1, 0}, {0, 0, 1}, {6, 0, -1}} v[1] = {0, 1, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[3]]
Abs[LinearRecurrence[{-1, 0, 6}, {0, 1, 1}, 40]] (* Vincenzo Librandi, Jun 28 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Jun 11 2005
EXTENSIONS
Edited by Robert Israel, Jun 27 2018
STATUS
approved