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A048788
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a(2n+1) = a(2n) + a(2n-1), a(2n) = 2*a(2n-1) + a(2n-2).
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10
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0, 1, 2, 3, 8, 11, 30, 41, 112, 153, 418, 571, 1560, 2131, 5822, 7953, 21728, 29681, 81090, 110771, 302632, 413403, 1129438, 1542841, 4215120, 5757961, 15731042, 21489003, 58709048, 80198051, 219105150, 299303201, 817711552, 1117014753
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Numerators of continued fraction convergests to sqrt(3) - 1. See A002530 for denominators. - N. J. A. Sloane (njas(AT)research.att.com), Dec 17 2007. Convergents are 1, 2/3, 3/4, 8/11, 11/15, 30/41, 41/56, 112/153, ...
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REFERENCES
| Marcia Edson, Scott Lewis and Omer Yayenie, THE K-PERIODIC FIBONACCI SEQUENCE AND AN EXTENDED BINET'S FORMULA, INTEGERS 11 (2011) #A32.
Russell Lyons, A birds-eye view of uniform spanning trees and forests, in Microsurveys in Discrete Probability, AMS, 1998.
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FORMULA
| G.f.: x(1+2x-x^2)/(1-4x+x^2).
G.f.: x(1+2x-x^2)/(1-4x^2+x^4). [From Paul Barry (pbarry(AT)wit.ie), Sep 18 2009]
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MATHEMATICA
| Numerator[NestList[(2/(2+#))&, 0, 60]] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 13 2010]
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CROSSREFS
| Cf. A002530, A002531.
Bisections are A001835 and A052530.
Sequence in context: A042263 A153439 A119064 * A143914 A041123 A042045
Adjacent sequences: A048785 A048786 A048787 * A048789 A048790 A048791
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KEYWORD
| nonn,easy,frac
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AUTHOR
| Robin Trew (trew(AT)hcs.harvard.edu).
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EXTENSIONS
| Corrected denonimator of g.f. [From Paul Barry (pbarry(AT)wit.ie), Sep 18 2009]
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