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A114552
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Odd-indexed bisection of A114551, which is the continued fraction expansion of Sum_{n>=0} 1/A112373(n); also, a(n) = A112373(n+1)/A112373(n) for n>=0.
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2
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OFFSET
| 0,2
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COMMENTS
| A112373 is defined by the recurrence: let b(n) = A112373(n), then
b(n) =(b(n-1)^3 + b(n-1)^2)/b(n-2) for n>=2 with b(0)=b(1)=1.
The next term is too large to include.
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FORMULA
| a(n) = a(n-1)*(1 + a(0)*a(1)*a(2)*...*a(n-1)) for n>=1, with a(0)=1.
a(n) = a(n-1)*(1 - a(n-1) + a(n-1)^2/a(n-2)) for n>=2, with a(0)=1, a(1)=2.
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EXAMPLE
| a(5) = 4999703411742 = 73086*(1 + 1*2*6*78*73086).
a(5) = a(4)*(1 - a(4) + a(4)^2/a(3)) = 73086*(1 - 73086 + 73086^2/78).
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PROG
| (PARI) a(n)=if(n==0, 1, if(n==1, 2, a(n-1)*(1-a(n-1)+a(n-1)^2/a(n-2))))
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CROSSREFS
| Cf. A112373, A114550 (constant), A114551 (continued fraction).
Sequence in context: A000721 A136306 A076146 * A055706 A118537 A109892
Adjacent sequences: A114549 A114550 A114551 * A114553 A114554 A114555
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 08 2005
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