|
%I #12 Jun 20 2018 08:37:59
%S 2,4,12,14,40,56,112,178,306,482,792,1214,1924,2914,4470,6706,10064,
%T 14924,22078,32382,47376,68862,99820,144002,207150,296896,424386,
%U 604802,859850,1219352,1725460,2436322,3433452,4829532,6781600,9506810,13306606,18597506,25956060,36177962
%N Number of maximal matchings in the n-dipyramidal graph.
%C Extended to a(1) using the recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0, 5, 3, -10, -12, 7, 18, 4, -11, -8, 1, 3, 1).
%F a(n) = 5*a(n-2) + 3*a(n-3) - 10*a(n-4) - 12*a(n-5) + 7*a(n-6) + 18*a(n-7) + 4*a(n-8) - 11*a(n-9) - 8*a(n-10) + a(n-11) + 3*a(n-12) + a(n-13).
%F G.f.: -2*(1 + 2*x + x^2 - 6*x^3 - 6*x^4 + 7*x^5 + 12*x^6 - x^7 - 9*x^8 - 6 x^9 + 2 x^11 + x^12)/((-1 + x^2)^2*(-1 + x^2 + x^3)^3).
%t LinearRecurrence[{0, 5, 3, -10, -12, 7, 18, 4, -11, -8, 1, 3, 1}, {2, 4, 12, 14, 40, 56, 112, 178, 306, 482, 792, 1214, 1924}, 20]
%t CoefficientList[Series[-2 (1 + 2 x + x^2 - 6 x^3 - 6 x^4 + 7 x^5 + 12 x^6 - x^7 - 9 x^8 - 6 x^9 + 2 x^11 + x^12)/((-1 + x^2)^2 (-1 + x^2 + x^3)^3), {x, 0, 20}], x]
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Jun 18 2018
|
