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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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2
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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, 53301709843200, 198924689265122, 742397047217292
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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O.g.f.: 2*x*(1+x)/((1-x)*(1-4*x+x^2)). - R. J. Mathar, Dec 05 2007
E.g.f.: 2*exp(x)*(exp(x)*cosh(sqrt(3)*x) - 1). - Stefano Spezia, May 05 2024
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MAPLE
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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
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MATHEMATICA
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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]
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PROG
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(PARI) x='x+O('x^99); Vec(2*x*(1+x)/((1-x)*(1-4*x+x^2))) \\ Altug Alkan, Mar 28 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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