A071895 CONTINUANT transform of Fibonacci number 1, 2, 3, 5, 8, ...

1, 3, 10, 53, 434, 5695, 120029, 4086681, 224887484, 20019072757, 2882971364492, 671752346999393, 253253517790135653, 154485317604329747723, 152477261728991251138254, 243506341466516632397539361, 629220538826740707106492847078, 2630771316340944362928878991172479

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

Essentially the same as A135829.

Sequence in context: A264409 A199202 A135829 * A054422 A074503 A318188

Adjacent sequences: A071892 A071893 A071894 * A071896 A071897 A071898

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2002

Status

approved