A290608 Number of maximal independent vertex sets (and minimal vertex covers) in the n-Moebius ladder graph.

2, 8, 12, 16, 30, 48, 74, 124, 200, 320, 522, 844, 1362, 2208, 3572, 5776, 9350, 15128, 24474, 39604, 64080, 103680, 167762, 271444, 439202, 710648, 1149852, 1860496, 3010350, 4870848, 7881194, 12752044, 20633240, 33385280, 54018522, 87403804, 141422322

Offset

3,1

Links

Table of n, a(n) for n=3..39.

Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Eric Weisstein's World of Mathematics, Minimal Vertex Cover

Eric Weisstein's World of Mathematics, Moebius Ladder

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

Formula

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

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

G.f.: -((2 x (1 + 4 x + 5 x^2 + 2 x^3))/(-1 + x^2 + 2 x^3 + x^4)).

Mathematica

Table[LucasL[n] - 2 Cos[2 n Pi/3], {n, 3, 20}]
LinearRecurrence[{0, 1, 2, 1}, {2, 8, 12, 16}, 20]
CoefficientList[Series[-((2 (1 + 4 x + 5 x^2 + 2 x^3))/(-1 + x^2 + 2 x^3 + x^4)), {x, 0, 20}], x]

Crossrefs

Cf. A000032.

Sequence in context: A284802 A067884 A005880 * A340690 A303900 A046470

Adjacent sequences: A290605 A290606 A290607 * A290609 A290610 A290611

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 07 2017

Status

approved