OFFSET
1,2
COMMENTS
Floor[a(n)/a(n-1)] = F(n+1). lim n->inf a(n)/a(n-1) = F(n+1). - Gerald McGarvey, Jul 17 2004, Nov 06 2007
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..75
N. J. A. Sloane, Transforms
FORMULA
For n > 2, a(n) = a(n-2) + F(n+1)*a(n-1). - Gerald McGarvey, Jul 17 2004
MAPLE
with(combinat):
a:= proc(n) option remember; `if`(n<0, 0,
`if`(n=0, 1, fibonacci(n+1) *a(n-1) +a(n-2)))
end:
seq(a(n), n=1..20); # Alois P. Heinz, Aug 06 2013
MATHEMATICA
a[1] = 1; a[2] = 3; a[n_] := a[n] = a[n-2] + Fibonacci[n+1]*a[n-1]; Array[a, 20] (* Jean-François Alcover, Feb 13 2016 *)
nxt[{n_, a_, b_}]:={n+1, b, a+b Fibonacci[n+2]}; NestList[nxt, {2, 1, 3}, 20][[;; , 2]] (* Harvey P. Dale, Mar 19 2024 *)
PROG
(Magma) I:=[1, 3]; [n le 2 select I[n] else Self(n-2)+Fibonacci(n+1)*Self(n-1): n in [1..20]]; // Vincenzo Librandi, Feb 13 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 10 2002
STATUS
approved