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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 W. Weisstein, Jul 16 2011 LINKS G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431. Anthony Flatters, Primitive Divisors of some Lehmer-Pierce Sequences, arXiv:0708.2190 [math.NT], 2007. Eric Weisstein's World of Mathematics, Gear Graph Eric Weisstein's World of Mathematics, Spanning Tree Index entries for linear recurrences with constant coefficients, signature (5, -5, 1). FORMULA a(2*n) = 12*A001353(n)^2, a(2*n+1) = 2*A001834(n)^2. - Vladeta Jovovic, May 30 2007 a(n) = 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 W. 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] LucasL[2 Range[20], Sqrt[2]] - 2 // Round (* Eric W. Weisstein, Mar 28 2018 *) PROG (PARI) x='x+O('x^99); Vec(2*x*(1+x)/((1-x)*(1-4*x+x^2))) \\ Altug Alkan, Mar 28 2018 CROSSREFS Cf. A001353, A001834, A092184. Sequence in context: A197891 A259802 A202789 * A115243 A218776 A241683 Adjacent sequences:  A129740 A129741 A129742 * A129744 A129745 A129746 KEYWORD nonn,easy 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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Last modified January 22 19:16 EST 2020. Contains 331153 sequences. (Running on oeis4.)