OFFSET
1,3
COMMENTS
All complement chordless cycles are of length 4.
LINKS
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Graph Complement
Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph
Index entries for linear recurrences with constant coefficients, signature (13,-39,27).
FORMULA
a(n) = (72-17*3^n+9^n)/2 for n > 1.
a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3) for n > 4.
G.f. -9*x^3*(19+45*x)/((-1+x)*(-1+3*x)*(-1+9*x)).
MATHEMATICA
Join[{0}, Table[(72 - 17 3^n + 9^n)/2, {n, 2, 10}]]
Join[{0}, LinearRecurrence[{13, -39, 27}, {0, 171, 2628}, 20]]
CoefficientList[Series[-9 x^2 (19 + 45 x)/((-1 + x) (-1 + 3 x) (-1 + 9 x)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Feb 14 2024
STATUS
approved