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%I #7 Dec 07 2024 10:42:04
%S 1,2,4,6,10,14,17,24,30,34,44,52,57,70,80,86,102,114,121,140,154,162,
%T 184,200,209,234,252,262,290,310,321,352,374,386,420,444,457,494,520,
%U 534,574,602,617,660,690,706,752,784,801,850,884,902,954,990,1009
%N Lower matching number of the (n,n)-stacked book graph.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LowerMatchingNumber.html">Lower Matching Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StackedBookGraph.html">Stacked Book Graph</a>.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F G.f.: x*(-1-x-2*x^2-2*x^4)/((-1+x)^3*(1+x+x^2)^2).
%F a(n) = 1*a(n-1)+2*a(n-3)-2*a(n-4)-1*a(n-6)+1*a(n-7).
%t Table[1/27 (6 + 6 n + 9 n^2 + 6 (n + 2) ChebyshevU[n, -1/2] + 3 (1 + n) ChebyshevU[n + 1, -1/2] - 15 Cos[2 n Pi/3] + 11 Sqrt[3] Sin[2 n Pi/3]), {n, 20}]
%t LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {1, 2, 4, 6, 10, 14, 17}, 20]
%t CoefficientList[Series[-(1 + x + 2 x^2 + 2 x^4)/((-1 + x)^3 (1 + x + x^2)^2), {x, 0, 20}], x]
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Dec 07 2024