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A085447
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a(n) = 6*a(n-1) + a(n-2), starting with a(0)=2 and a(1)=6.
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3
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2, 6, 38, 234, 1442, 8886, 54758, 337434, 2079362, 12813606, 78960998, 486579594, 2998438562, 18477210966, 113861704358, 701647437114, 4323746327042, 26644125399366, 164188498723238, 1011775117738794
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n+1)/a(n) converges to 3 + sqrt 10.
a(0)/a(1) = 1/3 = [3]; a(1)/a(2) = 6/38 = [6,3]; a(2)/a(3) = 38/234 = [6,6,3], a(3)/a(4) = 234/1442 = [6,6,6,3]; a(4)/a(5) = 1442/8886 = [6,6,6,6,3];...etc. Lim a(n)/a(n+1) as n approaches infinity = 0.1622776...= 1/(3 + sqrt10) = sqrt(10) - 3.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
| a(n) = (3 + sqrt 10)^n + (3 - sqrt 10)^n = A005668(n+1) + A005668(n-1).
O.g.f.: 2*(-1+3*x)/(-1+6*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 02 2007
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EXAMPLE
| a(4) = 1442 = 6*a(3)+a(2) = 6*234+38 =
(3+sqrt(10))^4+(3-sqrt(10))^4 = 1441.993...+0.0006... =
A005668(5)+A005668(3) = 1405+37.
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CROSSREFS
| Cf. A005668.
Sequence in context: A186648 A013033 A027322 * A078673 A052841 A197972
Adjacent sequences: A085444 A085445 A085446 * A085448 A085449 A085450
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 01 2003
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EXTENSIONS
| Edited and extended by Henry Bottomley (se16(AT)btinternet.com), Jul 13 2003
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