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A176343
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a(n) = Fibonacci(n)*a(n-1) + 1, a(0) = 0.
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5
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0, 1, 2, 5, 16, 81, 649, 8438, 177199, 6024767, 331362186, 29491234555, 4246737775921, 989489901789594, 373037692974676939, 227552992714552932791, 224594803809263744664718, 358677901683394200229554647, 926823697949890613393169207849
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MAPLE
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with(combinat);
a:= proc(n) option remember;
if n=0 then 0
else 1 + fibonacci(n)*a(n-1)
fi; end:
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MATHEMATICA
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a[n_]:= a[n]= If[n==0, 0, Fibonacci[n]*a[n-1] +1]; Table[a[n], {n, 0, 20}]
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PROG
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(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;
(Sage)
def a(n):
if (n==0): return 0
else: return 1 + fibonacci(n)*a(n-1)
(GAP)
a:= function(n)
if n=0 then return 0;
else return 1 + Fibonacci(n)*a(n-1);
fi; end;
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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