A297667 Number of chordless cycles in the n-Moebius ladder.

1, 6, 9, 12, 15, 22, 35, 56, 87, 134, 209, 332, 533, 858, 1381, 2224, 3587, 5794, 9367, 15148, 24499, 39626, 64101, 103704, 167785, 271470, 439233, 710676, 1149879, 1860526, 3010379, 4870880, 7881231, 12752078, 20633273, 33385316, 54018557, 87403842, 141422365, 228826168

Offset

1,2

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Chordless Cycle

Eric Weisstein's World of Mathematics, Moebius Ladder

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, 0, -2, 1).

Formula

a(n) = n - 2*cos(n*Pi/3) + Lucas(n).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 2*a(n-5) + a(n-6).

G.f.: x*(-1 - 2*x + 9*x^2 - 8*x^3 + 3*x^4)/((-1+x)^2 *(x^2+x-1) *(x^2-x+1)).

Mathematica

Table[n - 2 Cos[n Pi/3] + LucasL[n], {n, 20}]
LinearRecurrence[{4, -6, 4, 0, -2, 1}, {1, 6, 9, 12, 15, 22}, 20]
CoefficientList[Series[(-1 - 2 x + 9 x^2 - 8 x^3 + 3 x^4)/((-1 + x)^2 (-1 + 2 x - x^2 + x^4)), {x, 0, 20}], x]

Prog

(PARI) x='x+O('x^23); Vec((-1 - 2*x + 9*x^2 - 8*x^3 + 3*x^4)/((-1 + x)^2* (-1 + 2*x - x^2 + x^4))) \\ Georg Fischer, Apr 03 2019

Crossrefs

Sequence in context: A315953 A359613 A315954 * A315955 A315956 A343043

Adjacent sequences: A297664 A297665 A297666 * A297668 A297669 A297670

Keyword

nonn,easy

Author

Eric W. Weisstein, Jan 02 2018

Extensions

Terms a(1), a(2) prepended by Georg Fischer, Apr 03 2019

Status

approved