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 A129743 a(n) = -(u^n-1)*(v^n-1) with u = 2+sqrt(3), v = 2-sqrt(3). 1
 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; text; internal format)
 OFFSET 1,1 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 REFERENCES G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431. 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 FORMULA a(2*n) = 12*A001353(n)^2, a(2*n+1) =2*A001834(n)^2. - Vladeta Jovovic, May 30 2007 Equals 2*A092184(n). - Robert G. Wilson v, Jul 04 2007. O.g.f.: 2*x*(1+x)/((1-x)*(1-4*x+x^2)). - R. J. Mathar, Dec 05 2007 a(n) = +5*a(n-1)-5*a(n-2)+a(n-3). - Eric Weisstein, Jul 15 2011 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, May 13 2007 MATHEMATICA Table[-((2 + Sqrt[3])^n - 1)*((2 - Sqrt[3])^n - 1)], {n, 30}] // Expand - Stefan Steinerberger, May 15 2007 LinearRecurrence[{5, -5, 1}, {2, 12, 50}, 30] CROSSREFS Sequence in context: A003493 A197891 A202789 * A115243 A218776 A012423 Adjacent sequences:  A129740 A129741 A129742 * A129744 A129745 A129746 KEYWORD nonn,easy,changed AUTHOR N. J. A. Sloane, May 13 2007 EXTENSIONS More terms from Emeric Deutsch and Stefan Steinerberger, May 13 2007 More terms from Vladeta Jovovic, May 30 2007 STATUS approved

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