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A096656 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. 2
1, 2, 8, 46, 408, 5672, 124416, 4349256, 243439224, 21905300016, 3176029293240, 743169188527224, 280914798900088368, 171638202113128667928, 169578263512987049149416, 270985893735725975486862288 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) ~ c * ((1+sqrt(5))/2)^((n+2)*(n+3)/2) / 5^(n/2) where c = 0.5018252861856573838264566231631563920610293670131098212588... . - Vaclav Kotesovec, Nov 27 2015

EXAMPLE

a(2)=F(4)*2+F(3)*1=8, a(3)=F(5)*8+F(4)*2=46.

MATHEMATICA

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 *)

CROSSREFS

Cf. A000045, A096654, A096655.

Sequence in context: A007289 A099765 A246386 * A297014 A102009 A254747

Adjacent sequences:  A096653 A096654 A096655 * A096657 A096658 A096659

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 01 2004

EXTENSIONS

More terms from Robert G. Wilson v, Jul 09 2004

STATUS

approved

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Last modified October 19 16:08 EDT 2019. Contains 328223 sequences. (Running on oeis4.)