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A129743
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a(n) = -(u^n-1)*(v^n-1) with u = 2+sqrt(3), v = 2-sqrt(3).
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1
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2, 12, 50, 192, 722, 2700, 10082, 37632, 140450, 524172, 1956242, 7300800, 27246962, 101687052, 379501250, 1416317952, 5285770562, 19726764300, 73621286642, 274758382272, 1025412242450, 3826890587532, 14282150107682
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Each term of this sequence beyond the sixth has a primitive prime divisor. - Anthony Flatters (Anthony.Flatters(AT)uea.ac.uk), Aug 17 2007
a(n) is also the number of spanning trees for the n-gear graph - Eric Weisstein, Jul 16 2011
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REFERENCES
| G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
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LINKS
| Anthony Flatters, Primitive Divisors of some Lehmer-Pierce Sequences, arXiv:0708.2190.
Eric Weisstein's World of Mathematics, Gear Graph
Eric Weisstein's World of Mathematics, Spanning Tree
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FORMULA
| a(2*n) = 12*A001353(n)^2, a(2*n+1) =2*A001834(n)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2007
Equals 2*A092184(n). - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 04 2007.
O.g.f.: 2*x*(1+x)/((1-x)*(1-4*x+x^2)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
a(n) = +5*a(n-1)-5*a(n-2)+a(n-3). - Eric Weisstein, Jul 15 2011
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MAPLE
| u:=2+sqrt(3): v:=2-sqrt(3): a:=n->expand(-(u^n-1)*(v^n-1)): seq(a(n), n=1..28); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2007
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MATHEMATICA
| Table[-((2 + Sqrt[3])^n - 1)*((2 - Sqrt[3])^n - 1)], {n, 30}] // Expand - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 15 2007
LinearRecurrence[{5, -5, 1}, {2, 12, 50}, 30]
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CROSSREFS
| Sequence in context: A003493 A197891 A202789 * A115243 A012423 A012427
Adjacent sequences: A129740 A129741 A129742 * A129744 A129745 A129746
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 13 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 13 2007
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2007
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