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%I #10 Sep 13 2017 11:12:32
%S 0,0,60,18336,840800,14629200,143939460,971877760,5018582016,
%T 21193207200,76518984300,243664127520,699965254560,1844973808496,
%U 4520720267700,10403885452800,22674321863680,47112768624960,93845538165276,180039346960800,333959821087200,600947653207440
%N Number of 6-cycles in the n X n rook complement graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
%F a(n) = (-2 + n)*(-1 + n)^2*n^2*(-52 + 12*n + 76*n^2 - 63*n^3 - 2*n^4 + 20*n^5 - 8*n^6 + n^7)/12.
%F a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13).
%F G.f.: (4 x^3 (-15 - 4389 x - 151778 x^2 - 1277962 x^3 - 3535266 x^4 - 3576650 x^5 - 1293586 x^6 - 137682 x^7 - 1883 x^8 + 11 x^9))/(-1 + x)^13.
%t Table[(-2 + n) (-1 + n)^2 n^2 (-52 + 12 n + 76 n^2 - 63 n^3 - 2 n^4 + 20 n^5 - 8 n^6 + n^7)/12, {n, 20}]
%t LinearRecurrence[{13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {0, 0, 60, 18336, 840800, 14629200, 143939460, 971877760, 5018582016, 21193207200, 76518984300, 243664127520, 699965254560}, 20]
%t CoefficientList[Series[(4 x^2 (-15 - 4389 x - 151778 x^2 - 1277962 x^3 - 3535266 x^4 - 3576650 x^5 - 1293586 x^6 - 137682 x^7 - 1883 x^8 + 11 x^9))/(-1 + x)^13, {x, 0, 20}], x]
%Y Cf. A179058 (3-cycles), A291910 (4-cycles), A291911 (5-cycles).
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Sep 05 2017
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