A107786 a(n) = |b(n)| where b(n) = -b(n-1) + 6*b(n-3) with b(0)=0, b(1)=1, b(2)=1.

0, 1, 1, 1, 7, 1, 5, 47, 53, 23, 259, 577, 715, 839, 4301, 8591, 3557, 22249, 73795, 95137, 38357, 481127, 1051949, 821807, 2064955, 8376649, 13307491, 917761, 49342133, 129187079, 134693645, 161359153, 936481627, 1744643497, 776488579

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

Sequence in context: A346610 A064467 A089204 * A246949 A154932 A026497

Adjacent sequences: A107783 A107784 A107785 * A107787 A107788 A107789

Keyword

nonn

Author

Roger L. Bagula, Jun 11 2005

Extensions

Edited by Robert Israel, Jun 27 2018

Status

approved