A089127 a(n+2) = F(n)*a(n+1) + F(n+1)*a(n) where F(n) = Fibonacci number (A000045) and a(0) = a(1) = 1.

1, 1, 1, 2, 4, 14, 62, 422, 4182, 63228, 1469976, 53456724, 3070947684, 281012112132, 41181274957380, 9701178631343304, 3682464921740427408, 2255878665570796559928, 2232433139398395667219512

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

Recurrence; a(n+2) = F(n) a(n+1) + F(n+1) a(n) where F(n) = Fibonacci number (A000045)

a(n) = determinant of the tridiagonal matrix of order n+1, where the subdiagonal is [-1,-1,...-1], the diagonal is [1,1,F(0),F(1),...,F(n-2)], and the superdiagonal is [F(0),F(1),...,F(n-1)] [Emanuele Munarini, Apr 17 2013]

Mathematica

a[n_] := a[n] = Fibonacci[n-2]a[n-1] + Fibonacci[n-1]a[n-2] a[0] = 1 a[1] = 1
RecurrenceTable[{a[0]==a[1]==1, a[n+2]==Fibonacci[n] a[n+1]+ Fibonacci[ n+1] a[n]}, a, {n, 20}] (* Harvey P. Dale, Sep 29 2016 *)

Prog

(Maxima) F(i, j) := if i=1 and j=1 then 1 elseif i=j+1 then -1 elseif i=j then fib(i-3) elseif i=j-1 then fib(i-1) else 0;
M(n):=genmatrix(lambda([i, j], F(i, j)), n+1, n+1);
  makelist(determinant(M(n)), n, 0, 12); [Emanuele Munarini, Apr 17 2013]

Crossrefs

Sequence in context: A132880 A019537 A046911 * A132852 A352644 A132079

Adjacent sequences: A089124 A089125 A089126 * A089128 A089129 A089130

Keyword

nonn

Author

Emanuele Munarini, Dec 05 2003

Status

approved