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A176343 a(n) = Fibonacci(n)*a(n-1) + 1, a(0) = 0. 5
0, 1, 2, 5, 16, 81, 649, 8438, 177199, 6024767, 331362186, 29491234555, 4246737775921, 989489901789594, 373037692974676939, 227552992714552932791, 224594803809263744664718, 358677901683394200229554647 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

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}]

PROG

(PARI) a(n) = if(n==0, 0, 1 + fibonacci(n)*a(n-1) ); \\ 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

(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

(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

CROSSREFS

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

Sequence in context: A236960 A290609 A048754 * A327062 A334157 A306020

Adjacent sequences:  A176340 A176341 A176342 * A176344 A176345 A176346

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Apr 15 2010

STATUS

approved

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Last modified December 2 01:23 EST 2020. Contains 338864 sequences. (Running on oeis4.)