A301773 Number of odd chordless cycles in the 2n-Moebius ladder graph.

0, 4, 8, 16, 48, 124, 320, 844, 2208, 5776, 15128, 39604, 103680, 271444, 710648, 1860496, 4870848, 12752044, 33385280, 87403804, 228826128, 599074576, 1568397608, 4106118244, 10749957120, 28143753124, 73681302248, 192900153616, 505019158608, 1322157322204

Offset

0,2

Comments

Sequence extended to a(0)-a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=0..29.

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 (2,1,2,-1).

Formula

a(n) = A005248(n) - 2*cos(2*n*Pi/3).

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

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

E.g.f.: 2*exp(-x/2)*(exp(2*x)*cosh(sqrt(5)*x/2) - cos(sqrt(3)*x/2)). - Stefano Spezia, Jul 21 2022

Mathematica

Table[LucasL[2 n] - 2 Cos[2 n Pi/3], {n, 0, 20}]
LinearRecurrence[{2, 1, 2, -1}, {0, 4, 8, 16}, 20]
CoefficientList[Series[-4 x (-1 + x^2)/(1 - 2 x - x^2 - 2 x^3 + x^4), {x, 0, 20}], x]

Crossrefs

Cf. A005248.

Sequence in context: A065978 A077447 A337783 * A102358 A038238 A230112

Adjacent sequences: A301770 A301771 A301772 * A301774 A301775 A301776

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 26 2018

Status

approved