A291915 Number of 6-cycles in the n-Fibonacci cube graph.

0, 0, 0, 2, 22, 82, 268, 742, 1902, 4562, 10452, 23068, 49432, 103364, 211764, 426354, 845626, 1655454, 3203876, 6137946, 11652946, 21944034, 41021256, 76174360, 140595760, 258061160, 471255240, 856536610, 1550048766, 2793774026, 5016560956, 8976350894

Offset: 1

Author

Eric W. Weisstein, Sep 05 2017

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..4737
• Ömer Egecioglu, Elif Saygı, and Zülfükar Saygı, The number of short cycles in Fibonacci cubes, Theoretical Computer Science (2021) Vol. 871, 134-146.
• Eric Weisstein's World of Mathematics, Fibonacci Cube Graph
• Eric Weisstein's World of Mathematics, Graph Cycle
• Index entries for linear recurrences with constant coefficients, signature (4,-2,-8,5,8,-2,-4,-1).

Crossrefs

Cf. A001628 (4-cycles).

Programs

Mathematica

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

Formula

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).