login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089126 a(n+2) = F(n+1)*a(n+1) + F(n)*a(n) where F(n) = Fibonacci number (A000045), a(0) = a(1) = 1. 2
1, 1, 1, 2, 5, 19, 110, 975, 13555, 297330, 10393875, 581772345, 52349401830, 7590091602225, 1776029657181945, 671331672100911690, 410181883162313724165, 405259031001185201881755, 647603522027573971050913590, 1674054699591760033962965879295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..99

Thotsaporn Aek Thanatipanonda and Yi Zhang, Sequences: Polynomial, C-finite, Holonomic, ..., arXiv:2004.01370 [math.CO], 2020.

FORMULA

Floor(a(n)/a(n-1)) = F(n-1) where F(n) = Fibonacci number. - Gerald McGarvey, Jul 17 2004

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

MATHEMATICA

a[n_] := a[n] = Fibonacci[n-1]*a[n-1] + Fibonacci[n-2]*a[n-2]; a[0] = 1; a[1] = 1;

PROG

(Maxima) F(i, j) := if i=j+1 then -1 elseif i=j then fib(i-2) elseif i=j-1 then fib(i-2) 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 */

(MAGMA) I:=[1, 1, 1]; [n le 3 select I[n] else Fibonacci(n-2)*Self(n-1)+Fibonacci(n-3)*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 27 2018

CROSSREFS

Cf. A000045.

Sequence in context: A328977 A224691 A192445 * A113346 A198945 A324168

Adjacent sequences:  A089123 A089124 A089125 * A089127 A089128 A089129

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Dec 05 2003

EXTENSIONS

a(18)-a(19) from Vincenzo Librandi, Feb 27 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 17:31 EST 2020. Contains 338807 sequences. (Running on oeis4.)