|
|
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.
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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):
|
|
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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|