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%I #31 Jan 28 2021 01:38:53
%S 3,15,51,191,708,2631,9775,36319,134943,501380,1862875,6921503,
%T 25716811,95550687,355018116,1319068095,4900991135,18209608887,
%U 67657713855,251381908996,934008268531,3470303209839,12893894812259,47907203888767,177998984624708,661354367518327,2457258957728079,9129933787225743,33922224882718431,126037862684586116
%N Number of matchings in the n-antiprism graph.
%C Antiprism graphs have n >= 3; sequence extended via recurrence to start at n = 1
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-1,-1).
%F a(n) = 3*a(n-1) + 3*a(n-2) - a(n-3) - a(n-4).
%F G.f.: -x*(-3-6*x+3*x^2+4*x^3)/(1-3*x-3*x^2+x^3+x^4).
%F a(n) = A073817(2*n). - _Greg Dresden_, Jan 27 2021
%t LinearRecurrence[{3, 3, -1, -1}, {3, 15, 51, 191}, 20]
%t Table[RootSum[1 + # - 3 #^2 - 3 #^3 + #^4 &, #^n &], {n, 20}]
%t CoefficientList[Series[(3 + 6 x - 3 x^2 - 4 x^3)/(1 - 3 x - 3 x^2 + x^3 + x^4), {x, 0, 20}], x]
%Y Bisection of A073817.
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Jul 09 2011
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