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A082766
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Series ratios converge alternately to sqrt(2) and 1+sqrt(1/2).
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4
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1, 1, 2, 3, 4, 7, 10, 17, 24, 41, 58, 99, 140, 239, 338, 577, 816, 1393, 1970, 3363, 4756, 8119, 11482, 19601, 27720, 47321, 66922, 114243, 161564, 275807, 390050, 665857, 941664, 1607521, 2273378, 3880899, 5488420, 9369319, 13250218, 22619537
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(2n+2)/a(2n+1) converges to sqrt(2).
a(2n+1)/a(2n) converges to 1+sqrt(1/2).
a(n+2)/a(n) converges to 1+sqrt(2).
a(2n) is A001333, a(2n+1) is A052542.
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FORMULA
| a(2n) = a(2n-1) + a(2n-2); a(2n+1) = a(2n) + a(2n-2)
O.g.f.: x(1-x^2+x)(x^2+1)/(1-2x^2-x^4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008]
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CROSSREFS
| Cf. A001333, A052542. See A119016 for another version.
Sequence in context: A051449 A018143 A136570 * A119016 A082958 A166012
Adjacent sequences: A082763 A082764 A082765 * A082767 A082768 A082769
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 24 2003
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Nov 04 2005
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