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%I #7 Nov 27 2015 05:35:23
%S 1,2,8,46,408,5672,124416,4349256,243439224,21905300016,3176029293240,
%T 743169188527224,280914798900088368,171638202113128667928,
%U 169578263512987049149416,270985893735725975486862288
%N a(n) = F(n+2)*a(n-1) + F(n+1)*a(n-2), where F = A000045 (Fibonacci numbers), a(0)=1, a(1)=2.
%C This is the sequence of denominators of self-convergents to the number 1.389805... whose self-continued fraction is (1,2,3,5,8,...) (Fibonacci numbers). See A096655 for numerators and A096654 for definitions.
%F a(n) ~ c * ((1+sqrt(5))/2)^((n+2)*(n+3)/2) / 5^(n/2) where c = 0.5018252861856573838264566231631563920610293670131098212588... . - _Vaclav Kotesovec_, Nov 27 2015
%e a(2)=F(4)*2+F(3)*1=8, a(3)=F(5)*8+F(4)*2=46.
%t a[0] = 1; a[1] = 2; a[n_] := Fibonacci[n + 2]*a[n - 1] + Fibonacci[n + 1]*a[n - 2]; Table[ a[n], {n, 0, 16}] (* _Robert G. Wilson v_, Jul 09 2004 *)
%Y Cf. A000045, A096654, A096655.
%K nonn
%O 0,2
%A _Clark Kimberling_, Jul 01 2004
%E More terms from _Robert G. Wilson v_, Jul 09 2004
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