|
%I #7 Mar 04 2024 00:32:46
%S 0,0,96,320,3200,4480,14336,43008,122880,337920,901120,2342912,
%T 5963776,14909440,36700160,89128960,213909504,508035072,1195376640,
%U 2789212160,6459228160,14856224768,33957085184
%N Number of 6-cycles in the n-folded cube graph.
%C a(5) is also the number of 6-cycles in the 2-Keller graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FoldedCubeGraph.html">Folded Cube Graph</a>
%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/KellerGraph.html">Keller 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)*n*(n - 1)*(n - 2)/3 for n > 6.
%F a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 10.
%F G.f.: 32*x^4*(3 - 14*x + 92*x^2 - 516*x^3 + 1456*x^4 - 1920*x^5 + 960*x^6)/(-1 + 2*x)^4.
%t Table[Piecewise[{{0, n == 3}, {96, n == 4}, {3200, n == 6}}, 2^(n - 1) n (n - 1) (n - 2)/3], {n, 2, 20}]
%t Join[{0, 0, 96, 320, 3200}, LinearRecurrence[{8, -24, 32, -16}, {4480, 14336, 43008, 122880, 337920}, 14]]
%t CoefficientList[Series[32 x^2 (3 - 14 x + 92 x^2 - 516 x^3 + 1456 x^4 - 1920 x^5 + 960 x^6)/(-1 + 2 x)^4, {x, 0, 20}], x]
%Y Cf. A052482 (4-cycles).
%K nonn,easy
%O 2,3
%A _Eric W. Weisstein_, Mar 21 2018
|
