A364605 Number of 6-cycles in the n-Lucas cube graph.

0, 0, 0, 0, 5, 44, 147, 464, 1236, 3100, 7293, 16472, 35919, 76216, 158040, 321472, 643229, 1268868, 2472147, 4764120, 9092300, 17202636, 32294277, 60199088, 111498175, 205306192, 376014960, 685273120, 1243205205, 2245893340, 4041415347, 7245914176, 12947137412

Offset

1,5

Links

Table of n, a(n) for n=1..33.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Lucas Cube Graph

Index entries for linear recurrences with constant coefficients, signature (4, -2, -8, 5, 8, -2, -4, -1).

Formula

a(n) = (n + 1)*(3*(40n^2 - 145*n + 99)*A000045(n) - (40*n^2 - 133*n + 75)*A000032(n))/150.

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) for n > 1.

G.f.: x^4*(5+24*x-19*x^2+4*x^3+x^4)/(-1+x+x^2)^4.

Mathematica

Join[{0}, Table[(n + 1) (3 (40 n^2 - 145 n + 99) Fibonacci[n] - (40 n^2 - 133 n + 75) LucasL[n])/150, {n, 20}]
Join[{0}, LinearRecurrence[{4, -2, -8, 5, 8, -2, -4, -1}, {0, 0, 0, 5, 44, 147, 464, 1236}, 20]]
CoefficientList[Series[x^4 (5 + 24 x - 19 x^2 + 4 x^3 + x^4)/(-1 + x + x^2)^4, {x, 0, 20}], x]

Crossrefs

Cf. A245961 (number of 4-cycles).

Sequence in context: A159298 A262118 A173376 * A128523 A366650 A271298

Adjacent sequences: A364602 A364603 A364604 * A364606 A364607 A364608

Keyword

nonn

Author

Eric W. Weisstein, Jul 30 2023

Status

approved