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%I #7 Jul 18 2017 15:27:44
%S 0,0,0,640,34720,533760,4735360,30822400,164183040,759521280,
%T 3163607040,12148899840,43724595200,149243494400,487404503040,
%U 1533406085120,4672095518720,13845292646400,40043324375040,113352785264640,314803035832320,859445521285120
%N Number of 6-cycles in the n-halved cube 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/HalvedCubeGraph.html">Halved Cube Graph</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (14, -84, 280, -560, 672, -448, 128).
%F a(n) = 2^n*binomial(n, 4)*(81*n^2 - 552*n + 952).
%F a(n) = 14*a(n-1)-84*a(n-2)+280*a(n-3)-560*a(n-4)+672*a(n-5)-448*a(n-6)+128*a(n-7).
%F G.f.: (-160*x*(4*x^3 + 161*x^4 + 634*x^5))/(-1 + 2*x)^7.
%t seq = Table[2^n Binomial[n, 4] (81 n^2 - 552 n + 952), {n, 30}]
%t LinearRecurrence[{14, -84, 280, -560, 672, -448, 128}, {0, 0, 0, 640, 34720, 533760, 4735360}, 20]
%t CoefficientList[
%t Series[-((160 (4 x^3 + 161 x^4 + 634 x^5))/(-1 + 2 x)^7), {x, 0,
%t 20}], x]
%Y Cf. A290026 (3-cycles), A290027 (4-cycles), A290028 (5-cycles).
%K nonn
%O 1,4
%A _Eric W. Weisstein_, Jul 17 2017
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