OFFSET
1,3
COMMENTS
Using the convention that chordless cycles have length >= 4.
All chordless cycles in the rook complement graph have a cycle length of either 4 or 6. - Andrew Howroyd, Mar 03 2023
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Rook Complement Graph
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = 2*binomial(n,2)*binomial(n,3) + 9*binomial(n,3)^2 + 12*binomial(n,4)*binomial(n,2). - Andrew Howroyd, Mar 03 2023
a(n) = (n - 2)*(n - 1)^2*n^2*(6*n - 13)/12.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
G.f.: x^3*(15+159*x+167*x^2+19*x^3)/(1-x)^7.
MATHEMATICA
Table[(n - 2) (n - 1)^2 n^2 (6 n - 13)/12, {n, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 15, 264, 1700, 6900, 21315}, 20]
CoefficientList[Series[x^2 (15 + 159 x + 167 x^2 + 19 x^3)/(1 - x)^7, {x, 0, 20}], x]
PROG
(PARI) a(n) = 2*binomial(n, 2)*binomial(n, 3) + 9*binomial(n, 3)^2 + 12*binomial(n, 4)*binomial(n, 2) \\ Andrew Howroyd, Mar 03 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 03 2023
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Mar 03 2023
STATUS
approved