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%I #6 Dec 07 2024 10:42:13
%S 0,2,3,6,8,14,17,24,28,38,43,54,60,74,81,96,104,122,131,150,160,182,
%T 193,216,228,254,267,294,308,338,353,384,400,434,451,486,504,542,561,
%U 600,620,662,683,726,748,794,817,864,888,938,963,1014,1040,1094,1121
%N Lower matching number of the n X n king graph.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LowerMatchingNumber.html">Lower Matching Number</a>.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1,-1,1).
%F G.f.: -(x^2*(2+x+x^2+x^3+x^4))/((-1+x)^3*(1+x)^2*(1+x^2)).
%F a(n) = 1*a(n-1)+1*a(n-2)-1*a(n-3)+1*a(n-4)-1*a(n-5)-1*a(n-6)+1*a(n-7).
%t Table[(3 + (-1)^n + 2 n (-1 + (-1)^n + 3 n) - 4 Cos[n Pi/2] - 4 Sin[n Pi/2])/16, {n, 20}]
%t LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {0, 2, 3, 6, 8, 14, 17}, 20]
%t CoefficientList[Series[-((x (2 + x + x^2 + x^3 + x^4))/((-1 + x)^3 (1 + x)^2 (1 + x^2))), {x, 0, 20}], x]
%K nonn,new
%O 1,2
%A _Eric W. Weisstein_, Dec 07 2024