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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. 1
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

Table of n, a(n) for n=0..19.

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

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

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Last modified February 26 08:14 EST 2020. Contains 332277 sequences. (Running on oeis4.)