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A071895 CONTINUANT transform of Fibonacci number 1, 2, 3, 5, 8, ... 3
1, 3, 10, 53, 434, 5695, 120029, 4086681, 224887484, 20019072757, 2882971364492, 671752346999393, 253253517790135653, 154485317604329747723, 152477261728991251138254, 243506341466516632397539361, 629220538826740707106492847078, 2630771316340944362928878991172479 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 13 2016 *)

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

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)