login
Number of 6-cycles in the n-Fibonacci cube graph.
2

%I #10 Aug 19 2021 01:02:08

%S 0,0,0,2,22,82,268,742,1902,4562,10452,23068,49432,103364,211764,

%T 426354,845626,1655454,3203876,6137946,11652946,21944034,41021256,

%U 76174360,140595760,258061160,471255240,856536610,1550048766,2793774026,5016560956,8976350894

%N Number of 6-cycles in the n-Fibonacci cube graph.

%H Michael De Vlieger, <a href="/A291915/b291915.txt">Table of n, a(n) for n = 1..4737</a>

%H Ömer Egecioglu, Elif Saygı, and Zülfükar Saygı, <a href="https://doi.org/10.1016/j.tcs.2021.04.019">The number of short cycles in Fibonacci cubes</a>, Theoretical Computer Science (2021) Vol. 871, 134-146.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciCubeGraph.html">Fibonacci Cube Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-8,5,8,-2,-4,-1).

%F a(n) = 4*a(n-1) - 2*a(n-2) - 8*a(n-3) + 5*a(n-4) + 8*a(n-5) - 2*a(n-6) - 4*a(n-7) - a(n-8).

%t LinearRecurrence[{4, -2, -8, 5, 8, -2, -4, -1}, {0, 0, 0, 2, 22, 82, 268, 742}, 40]

%Y Cf. A001628 (4-cycles).

%K nonn,easy

%O 1,4

%A _Eric W. Weisstein_, Sep 05 2017