A367644 Number of maximal independent vertex sets and minimal vertex covers in the n-trapezohedral graph.

3, 3, 6, 11, 18, 30, 52, 91, 159, 278, 487, 854, 1498, 2628, 4611, 8091, 14198, 24915, 43722, 76726, 134644, 236283, 414647, 727654, 1276943, 2240878, 3932466, 6900996, 12110403, 21252275, 37295142, 65448411, 114853954, 201554638, 353703732, 620706779

Offset

1,1

Comments

Extended to n=1 using the formula/recurrence.

Links

Table of n, a(n) for n=1..36.

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, Trapezohedral Graph

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-1).

Formula

a(n) = A001608(2n) + 1.

a(n) = A109377(n+2) + 1.

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

G.f.: x*(3-6*x+6*x^2-4*x^3)/(1-3*x+3*x^2-2*x^3+x^4).

Mathematica

Table[1 + RootSum[-1 + # - 2  #^2 + #^3 &, #^n &], {n, 0, 20}]
LinearRecurrence[{3, -3, 2, -1}, {3, 3, 6, 11}, 20]
CoefficientList[Series[(3 - 6 x + 6 x^2 - 4 x^3)/(1 - 3 x + 3 x^2 - 2 x^3 + x^4), {x, 0, 20}], x]

Crossrefs

Cf. A001608, A109377.

Sequence in context: A339539 A025250 A326498 * A094305 A360850 A360202

Adjacent sequences: A367641 A367642 A367643 * A367645 A367646 A367647

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 25 2023

Status

approved