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

0,2

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

Table of n, a(n) for n=0..25.

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

Cf. A002203 (companion Pell numbers).

Sequence in context: A133718 A241696 A052255 * A082203 A367118 A101102

Adjacent sequences: A362542 A362543 A362544 * A362546 A362547 A362548

Keyword

nonn

Author

Eric W. Weisstein, Apr 24 2023

Status

approved