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%I #20 Mar 19 2024 09:24:45
%S 1,3,10,53,434,5695,120029,4086681,224887484,20019072757,
%T 2882971364492,671752346999393,253253517790135653,
%U 154485317604329747723,152477261728991251138254,243506341466516632397539361,629220538826740707106492847078,2630771316340944362928878991172479
%N CONTINUANT transform of Fibonacci number 1, 2, 3, 5, 8, ...
%C 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
%H Alois P. Heinz, <a href="/A071895/b071895.txt">Table of n, a(n) for n = 1..75</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F For n > 2, a(n) = a(n-2) + F(n+1)*a(n-1). - _Gerald McGarvey_, Jul 17 2004
%p with(combinat):
%p a:= proc(n) option remember; `if`(n<0, 0,
%p `if`(n=0, 1, fibonacci(n+1) *a(n-1) +a(n-2)))
%p end:
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Aug 06 2013
%t 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 *)
%t 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 *)
%o (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
%Y Essentially the same as A135829.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jun 10 2002
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