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A020877
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Number of matchings in Moebius ladder M_n.
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3
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10, 34, 106, 344, 1102, 3546, 11394, 36628, 117730, 378426, 1216378, 3909832, 12567446, 40395794, 129844994, 417363332, 1341539194, 4312135922, 13860583626, 44552347608, 143205490526, 460308235562, 1479577849602, 4755836293844, 15286778495570, 49136593930954
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OFFSET
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2,1
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COMMENTS
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LINKS
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Eric Weisstein's World of Mathematics, Matching
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FORMULA
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G.f.: 2*x^2*(5+7*x-x^2-2*x^3)/((1+x)*(1-3*x-x^2+x^3)). - Emeric Deutsch, Dec 21 2004
The McSorley reference gives the approximation a(n)~(3.2143)^n+(-0.6751)^n+(0.4608)^n-(-1)^n. - Emeric Deutsch, Dec 21 2004
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MAPLE
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G:=2*x^2*(5+7*x-x^2-2*x^3)/(1+x)/(1-3*x-x^2+x^3): Gser:=series(G, x=0, 29): seq(coeff(Gser, x^n), n=2..27); # Emeric Deutsch, Dec 21 2004
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MATHEMATICA
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Table[RootSum[1 - # - 3 #^2 + #^3 &, #^n &] - (-1)^n, {n, 2, 20}] (* Eric W. Weisstein, Mar 31 2017 *)
LinearRecurrence[{2, 4, 0, -1}, {10, 34, 106, 344}, 20] (* Eric W. Weisstein, Mar 31 2017 *)
CoefficientList[Series[-2 (-5 - 7 x + x^2 + 2 x^3)/(1 - 2 x - 4 x^2 + x^4), {x, 0, 20}], x] (* Eric W. Weisstein, Oct 03 2017 *)
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PROG
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(PARI) Vec(-2*x^2*(2*x^3+x^2-7*x-5)/((x+1)*(x^3-x^2-3*x+1)) + O(x^50)) \\ Colin Barker, Aug 01 2015
(Magma) I:=[10, 34, 106, 344]; [n le 4 select I[n] else 2*Self(n-1)+4*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 07 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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