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Search: id:A096656
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| A096656 |
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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. |
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+0
3
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| 1, 2, 8, 46, 408, 5672, 124416, 4349256, 243439224, 21905300016, 3176029293240, 743169188527224, 280914798900088368, 171638202113128667928, 169578263512987049149416, 270985893735725975486862288
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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EXAMPLE
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a(2)=F(4)*2+F(3)*1=8, a(3)=F(5)*8+F(4)*2=46.
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MATHEMATICA
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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}] (from Robert G. Wilson v Jul 09 2004)
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CROSSREFS
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Cf. A000045, A096654, A096655.
Sequence in context: A074599 A007289 A099765 this_sequence A102009 A135904 A145846
Adjacent sequences: A096653 A096654 A096655 this_sequence A096657 A096658 A096659
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jul 01 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 09 2004
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