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A364605 Number of 6-cycles in the n-Lucas cube graph. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
LINKS
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 30 2023
STATUS
approved

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Last modified July 14 19:09 EDT 2024. Contains 374323 sequences. (Running on oeis4.)