%I #7 Jul 18 2017 15:29:56
%S 0,0,3,102,900,5160,23520,92736,330624,1094400,3421440,10222080,
%T 29432832,82188288,223641600,595230720,1554186240,3990749184,
%U 10097197056,25214976000,62234296320,151993712640,367691563008,881823055872,2098200576000,4956409036800
%N Number of 4-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_05">Index entries for linear recurrences with constant coefficients</a>, signature (10, -40, 80, -80, 32).
%F a(n) = 3*2^(n-5)*binomial(n,3)*(13*n-35).
%F a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5).
%F G.f.: (-3*x*(x^2 + 24*x^3))/(-1 + 2*x)^5.
%t Table[3 2^(n - 5) Binomial[n, 3] (13 n - 35), {n, 20}]
%t LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 3, 102, 900}, 20]
%t CoefficientList[Series[-((3 (x^2 + 24 x^3))/(-1 + 2 x)^5), {x, 0, 20}], x]
%Y Cf. A290026 (3-cycles), A290028 (5-cycles), A290029 (6-cycles).
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Jul 17 2017
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