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A161728
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a(n) = ((3+sqrt(3))*(4+sqrt(3))^n-(3-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
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3
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1, 7, 43, 253, 1465, 8431, 48403, 277621, 1591729, 9124759, 52305595, 299822893, 1718610409, 9851185663, 56467549987, 323674986277, 1855321740385, 10634799101479, 60959210186827, 349421293175389, 2002900612974361
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fourth binomial transform of A162436, inverse binomial transform of A162272.
The inverse Binomial transform yields A030192. The Binomial transform yields A162272. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 07 2009]
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FORMULA
| a(n) = 8*a(n-1)-13(n-2) for n > 1; a(0) = 1, a(1) = 7.
G.f.: (1-x)/(1-8*x+13*x^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 19 2009]
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PROG
| (PARI) {default(debug, 0); F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((3+x)*(4+x)^n-(3-x)*(4-x)^n), (2*x))[1], ", "))} [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 19 2009]
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CROSSREFS
| Cf. A162436, A162272.
Sequence in context: A163869 A043553 A049609 * A003464 A022036 A015451
Adjacent sequences: A161725 A161726 A161727 * A161729 A161730 A161731
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
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EXTENSIONS
| Extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 19 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 05 2009
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