A362545 Number of odd chordless cycles of length >4 in the (2n+1)-flower snark.

1, 13, 81, 477, 2785, 16237, 94641, 551613, 3215041, 18738637, 109216785, 636562077, 3710155681, 21624372013, 126036076401, 734592086397, 4281516441985, 24954506565517, 145445522951121, 847718631141213, 4940866263896161, 28797478952235757, 167844007449518385, 978266565744874557, 5701755387019728961, 33232265756373499213

Offset: 0

Author

Eric W. Weisstein, Apr 24 2023

Keywords

• nonn

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).

Crossrefs

Cf. A002203 (companion Pell numbers).

Programs

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]

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)).