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A163302
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Numerators of fractions in the approximation of the square root of 5 satisfying: a(n)= (a(n-1)+ c)/(a(n-1)+1); with c=5 and a(1)=1. Also product of the Lucas numbers and the powers of 2.(Excluding the first Lucas Number(2))
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1, 6, 16, 56, 176, 576, 1856, 6016, 19456, 62976, 203776, 659456, 2134016, 6905856, 22347776, 72318976, 234029056
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For denominators, see A063727, which are the product of the powers of 2 and the Fibonacci sequence.
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FORMULA
| Reciprocal formula: a(n)=(a(n-1)+1)/(c*a(n-1)); with a(1)=1 [Reversed formula for accelerated approximation of Phi: a'(n)=(a(n-1)+1)/(a(n-1)+c); a'(n)=(c*a(n-1))/(a(n-1)+1); with c=2] [From M.Dols (markdols99(AT)yahoo.com), Jul 28 2009]
Empirical G.f. and recurrence: x*(1+4*x)/(1-2*x-4*x^2), a(n)=2*a(n-1)+4*a(n-2). - Colin Barker, Feb 08 2012
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CROSSREFS
| A000032, A000079, A084057, A063727, A000045
Sequence in context: A175659 A192000 A032282 * A084057 A091649 A125628
Adjacent sequences: A163299 A163300 A163301 * A163303 A163304 A163305
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KEYWORD
| nonn,changed
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AUTHOR
| Mark Dols (markdols99(AT)yahoo.com), Jul 24 2009
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