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Number of 6-cycles in the n X n queen graph.
3

%I #13 Jul 18 2017 10:34:18

%S 0,0,976,26414,207136,951750,3190304,8721576,20615340,43736788,

%T 85332868,155691014,268995384,444000894,705336724,1083967932,

%U 1619250600,2358809948,3361809572,4697700286,6451359236,8719953330,11620829368

%N Number of 6-cycles in the n X n queen 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/QueenGraph.html">Queen Graph</a>

%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (0, 3, 2, -1, -5, -6, -1, 6, 11, 6, -4, -10, -10, -4, 6, 11, 6, -1, -6, -5, -1, 2, 3, 0, -1).

%F a(n)=3*a(n-2)+2*a(n-3)-a(n-4)-5*a(n-5)-6*a(n-6)-a(n-7)+6*a(n-8)+11*a(n-9)+6*a(n-10)-4*a(n-11)-10*a(n-12)-10*a(n-13)-4*a(n-14)+6*a(n-15)+11*a(n-16)+6*a(n-17)-a(n-18)-6*a(n-19)-5*a(n-20)-a(n-21)+2*a(n-22)+3*a(n-23)-a(n-25).

%t LinearRecurrence[{0, 3, 2, -1, -5, -6, -1, 6, 11, 6, -4, -10, -10, -4, 6, 11, 6, -1, -6, -5, -1, 2, 3, 0, -1}, {0, 0, 976, 26414, 207136, 951750, 3190304, 8721576, 20615340, 43736788, 85332868, 155691014, 268995384, 444000894, 705336724, 1083967932, 1619250600, 2358809948,3361809572, 4697700286, 6451359236, 8719953330, 11620829368, 15285494276, 19871396864}, 30]

%Y Cf. A144298 (3-cycles), A156001 (4-cycles), A288916 (5-cycles).

%K nonn,easy

%O 1,3

%A _Eric W. Weisstein_, Jun 19 2017