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Search: id:A068204
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| A068204 |
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Let (x_n, y_n) be n-th solution to the Pell equation x^2 = 14*y^2 + 1. Sequence gives {y_n}. |
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+0
2
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| 4, 120, 3596, 107760, 3229204, 96768360, 2899821596, 86897879520, 2604036564004, 78034199040600, 2338421934653996, 70074623840579280, 2099900293282724404, 62926934174641152840, 1885708124945951860796
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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H. W. Lenstra Jr., Solving the Pell Equation, Notices Amer. Math. Soc., 49 (No. 2, 2002), 182-192.
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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x_n + y_n*sqrt(14) = (x_1 + y_1*sqrt(14))^n.
a(n) = (2+15/28*sqrt(14))*(-1/(-15-4*sqrt(14)))^n/(-15-4*sqrt(14))+(-15/28*sqrt(14)+2)*(-1/(-15+4*sqrt(14)))^n/(-15+4*sqrt(14)). Recurrence: a(n) = 30*a(n-1)-a(n-2). G.f.: 4*x/(1-30*x+x^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 25 2002
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MAPLE
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Digits := 1000: q := seq(floor(evalf(((15+4*sqrt(14))^n-(15-4*sqrt(14))^n)/28*sqrt(14))+0.1), n=1..30);
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CROSSREFS
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Cf. A068203.
Sequence in context: A054644 A006434 A002702 this_sequence A001332 A071304 A006607
Adjacent sequences: A068201 A068202 A068203 this_sequence A068205 A068206 A068207
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 24 2002
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EXTENSIONS
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More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 25 2002
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 25 2002
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