OFFSET
1,2
COMMENTS
Chordless cycles are all of length 4.
LINKS
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) = 3/2*(16-108*n+155*n^2-57*n^3+3*n^4-6*n^5+3*n^6) for n > 2.
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) for n > 2.
G.f.: (-3*x^2*(2+246*x+886*x^2-145*x^3+41*x^4+71*x^5-25*x^6+4*x^7))/(-1+x)^7.
MATHEMATICA
Table[Piecewise[{{0, n == 1}, {6, n == 2}}, 3/2 (16 - 108 n + 155 n^2 - 57 n^3 + 3 n^4 - 6 n^5 + 3 n^6)], {n, 20}]
CoefficientList[Series[-((3 x (2 + 246 x + 886 x^2 - 145 x^3 + 41 x^4 + 71 x^5 - 25 x^6 + 4 x^7))/(-1 + x)^7), {x, 0, 20}], x]
Join[{0, 6}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {780, 7992, 39339, 134754, 369918, 873000, 1844637}, 18]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 17 2023
EXTENSIONS
a(9) from Eric W. Weisstein, Aug 02 2023
a(10) and beyond from Eric W. Weisstein, Aug 15-16 2023
STATUS
approved