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%I #16 Oct 08 2019 22:05:20
%S 0,0,4,32,160,640,2240,7168,21504,61440,168960,450560,1171456,2981888,
%T 7454720,18350080,44564480,106954752,254017536,597688320,1394606080,
%U 3229614080,7428112384,16978542592,38587596800,87241523200,196293427200,439697276928,980863156224
%N Number of 3-cycles in the n-halved cube graph.
%C a(n) is the number of diagonals of length sqrt(3) in an n-cube. - _Nigel Stepp_, Oct 06 2019
%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_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F a(n) = 2^(n-1)*binomial(n,3).
%F a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4).
%F G.f.: (4*x^3)/(-1 + 2*x)^4.
%t Table[2^(n - 1) Binomial[n, 3], {n, 20}]
%t LinearRecurrence[{8, -24, 32, -16}, {0, 0, 4, 32}, 20]
%t CoefficientList[Series[(4 x^2)/(-1 + 2 x)^4, {x, 0, 20}], x]
%Y Cf. A290027 (4-cycles), A290028 (5-cycles), A290029 (6-cycles).
%K nonn,easy
%O 1,3
%A _Eric W. Weisstein_, Jul 17 2017
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