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%I #21 Jul 13 2021 00:22:58
%S 0,0,6,12,24,36,54,72,96,120,150,180,216,252,294,336,384,432,486,540,
%T 600,660,726,792,864,936,1014,1092,1176,1260,1350,1440,1536,1632,1734,
%U 1836,1944,2052,2166,2280,2400,2520,2646,2772,2904,3036,3174,3312,3456,3600,3750
%N Crossing number of the complete bipartite graph K_{6,n}.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCrossingNumber.html">Graph Crossing Number</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n) = 6*floor(n/2)*floor((n-1)/2).
%F G.f.: -6*x^3/((-1 + x)^3*(1 + x)).
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F a(n) = (3/4)*(2*n*(n - 2) + 1 - (-1)^n).
%F a(n) = 6*A002620(n-1). - _R. J. Mathar_, Feb 12 2021
%t Table[6 Floor[n/2] Floor[(n - 1)/2], {n, 60}]
%t Table[3/4 (2 n (n - 2) + 1 - (-1)^n), {n, 60}]
%t LinearRecurrence[{2, 0, -2, 1}, {0, 0, 6, 12}, 60]
%t CoefficientList[Series[-6 x^2/((-1 + x)^3 (1 + x)), {x, 0, 60}], x]
%o (PARI) a(n)=n--^2\4*6 \\ _Charles R Greathouse IV_, Jul 13 2021
%K nonn,easy
%O 1,3
%A _Eric W. Weisstein_, Sep 11 2018
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