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%I #20 Sep 11 2018 12:07:56
%S 0,0,0,0,0,2,4,6,8,12,16,20,24,30,36,42,48,56,64,72,80,90,100,110,120,
%T 132,144,156,168,182,196,210,224,240,256,272,288,306,324,342,360,380,
%U 400,420,440,462,484,506,528,552,576,600,624,650,676,702,728,756,784,812,840,870,900,930,960,992,1024,1056,1088,1122,1156,1190,1224,1260,1296,1332,1368
%N a(n) = 2*floor(n/4)*(n - 2*(1 + floor(n/4))).
%H Pak Tung Ho, <a href="https://doi.org/10.1016/j.disc.2008.09.029">The toroidal crossing number of K_{4,n}</a>, Discrete Math. 309 (2009), no. 10, 3238--3248. MR2526742(2010i:05088).
%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/ToroidalCrossingNumber.html">Toroidal Crossing Number</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).
%F From _R. J. Mathar_, Jun 28 2012: (Start)
%F G.f. -2*x^5 / ( (x + 1)*(x^2 + 1)*(x - 1)^3 ).
%F a(n) = 2*A001972(n-5) = 2*A130519(n-1). (End)
%F a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6). - _Eric W. Weisstein_, Sep 11 2018
%t Table[2 Floor[n/4] (n - 2 (1 + Floor[n/4])), {n, 0, 20}] (* or *)
%t Table[(5 - (-1)^n + 2 (n - 4) n - 4 Cos[n Pi/2])/8, {n, 0, 20}] (* or *)
%t Table[(5 - (-1)^n - 2 (-I)^n - 2 I^n - 8 n + 2 n^2)/8, {n, 0, 20}] (* or *)
%t LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 2}, 80] (* or *)
%t CoefficientList[Series[-2 x^5/((-1 + x)^3 (1 + x + x^2 + x^3)), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 11 2018 *)
%Y Cf. A001972, A130519.
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_, May 05 2012
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