OFFSET
0,2
COMMENTS
Sequence extended to n=0 using formula/recurrence.
The (2n)-flower graphs, which generalize the (2n+1)-flower snarks, have no odd chordless cycles of length >=4.
LINKS
Eric Weisstein's World of Mathematics, Flower Snark
Eric Weisstein's World of Mathematics, Odd Chordless Cycle
Index entries for linear recurrences with constant coefficients, signature (7,-7,1).
FORMULA
a(n) = LucasL(2 n + 1, 2) - 1.
a(n) = 7*a(n-1) - 7*a(n-1) + a(n-2).
G.f.: (-1 - 6*x + 3*x^2)/((-1 + x)*(1 - 6*x + x^2)).
MATHEMATICA
LucasL[2 Range[0, 20] + 1, 2] - 1
Table[LucasL[2 n + 1, 2] - 1, {n, 0, 20}]
LinearRecurrence[{7, -7, 1}, {1, 13, 81}, 20]
CoefficientList[Series[(-1 - 6 x + 3 x^2)/((-1 + x) (1 - 6 x + x^2)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 24 2023
STATUS
approved