A176343 a(n) = Fibonacci(n)*a(n-1) + 1, a(0) = 0.

0, 1, 2, 5, 16, 81, 649, 8438, 177199, 6024767, 331362186, 29491234555, 4246737775921, 989489901789594, 373037692974676939, 227552992714552932791, 224594803809263744664718, 358677901683394200229554647, 926823697949890613393169207849

Offset: 0

Author

Roger L. Bagula, Apr 15 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000045, A003266, A062073, A101689, A139339, A238243, A238244.

Programs

GAP

a:= function(n)
    if n=0 then return 0;
    else return 1 + Fibonacci(n)*a(n-1);
    fi; end;
List([0..20], n-> a(n) ); # G. C. Greubel, Dec 07 2019

Magma

function a(n)
  if n eq 0 then return 0;
  else return 1 + Fibonacci(n)*a(n-1);
  end if; return a; end function;
[a(n): n in [0..20]]; // G. C. Greubel, Dec 07 2019

Maple

with(combinat);
a:= proc(n) option remember;
      if n=0 then 0
    else 1 + fibonacci(n)*a(n-1)
      fi; end:
seq( a(n), n=0..20); # G. C. Greubel, Dec 07 2019

Mathematica

a[n_]:= a[n]= If[n==0, 0, Fibonacci[n]*a[n-1] +1]; Table[a[n], {n,0,20}]

PARI

a(n) = if(n==0, 0, 1 + fibonacci(n)*a(n-1) ); \\ G. C. Greubel, Dec 07 2019

Sage

def a(n):
    if (n==0): return 0
    else: return 1 + fibonacci(n)*a(n-1)
[a(n) for n in (0..20)] # G. C. Greubel, Dec 07 2019

Formula

a(n) = Fibonacci(n)*a(n-1) + 1, a(0) = 0.

a(n) ~ c * ((1+sqrt(5))/2)^(n^2/2+n/2) / 5^(n/2), where c = A062073 * A101689 = 3.317727324507285486862890025085971028467... is product of Fibonacci factorial constant (see A062073) and Sum_{n>=1} 1/(Product_{k=1..n} A000045(k) ). - Vaclav Kotesovec, Feb 20 2014