|
|
A288960
|
|
Number of 6-cycles in the n X n rook graph.
|
|
3
|
|
|
0, 0, 60, 1248, 8400, 35520, 114660, 309120, 731808, 1569600, 3114540, 5802720, 10261680, 17367168, 28310100, 44674560, 68527680, 102522240, 150012828, 215186400, 303208080, 420383040, 574335300, 774204288, 1030860000, 1357137600, 1768092300, 2281275360, 2917032048, 3698822400
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n-1)*(n-2)*n^2*(n+2)*(n^2+2*n-11)/6.
a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)+a(n-8).
G.f.: (12*x^3*(5+64*x+8*x^2-8*x^3+x^4))/(-1+x)^8.
|
|
MATHEMATICA
|
Table[(n - 1) (n - 2) n^2 (n + 2) (n^2 + 2 n - 11)/6, {n, 20}]
Table[Binomial[n, 3] n (n + 2) (n^2 + 2 n - 11), {n, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 60, 1248, 8400, 35520, 114660, 309120}, 20]
CoefficientList[Series[(12 x^2 (5 + 64 x + 8 x^2 - 8 x^3 + x^4))/(-1 + x)^8, {x, 0, 20}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|