A290698 Number of minimal edge covers in the n-antiprism graph.

2, 14, 74, 286, 1157, 4778, 19623, 80478, 330293, 1355629, 5563527, 22832914, 93707772, 384582275, 1578347684, 6477630782, 26584574434, 109104640685, 447771795953, 1837681518261, 7541951930181, 30952609765223, 127031312347552, 521343900861138

Offset

1,1

Comments

The n-antiprism graph is well defined for n >= 3. Sequence extended to n = 1 using recurrence. - Andrew Howroyd, Aug 10 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Minimal Edge Cover

Index entries for linear recurrences with constant coefficients, signature (2, 5, 12, 11, 5, -3, -4, -1, 1).

Formula

From Andrew Howroyd, Aug 10 2017: (Start)

a(n) = 2*a(n-1) + 5*a(n-2) + 12*a(n-3) + 11*a(n-4) + 5*a(n-5) - 3*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9).

G.f.: x*(2 + 10*x + 36*x^2 + 44*x^3 + 25*x^4 - 18*x^5 - 28*x^6 - 8*x^7 + 9*x^8)/((1 - 3*x - 3*x^2 - 6*x^3 - 2*x^4 + 3*x^5 + 2*x^6 - x^7)*(1 + x + x^2)).

(End)

Mathematica

Table[2 Cos[2 n Pi/3] + RootSum[-1 + 2 # + 3 #^2 - 2 #^3 - 6 #^4 - 3 #^5 - 3 #^6 + #^7 &, #^n &], {n, 20}]
LinearRecurrence[{2, 5, 12, 11, 5, -3, -4, -1, 1}, {2, 14, 74, 286, 1157, 4778, 19623, 80478, 330293}, 20]
CoefficientList[Series[(-2 - 10 x - 36 x^2 - 44 x^3 - 25 x^4 + 18 x^5 + 28 x^6 + 8 x^7 - 9 x^8)/(-1 + 2 x + 5 x^2 + 12 x^3 + 11 x^4 + 5 x^5 - 3 x^6 - 4 x^7 - x^8 + x^9), {x, 0, 20}], x]

Prog

(PARI)
Vec((2 + 10*x + 36*x^2 + 44*x^3 + 25*x^4 - 18*x^5 - 28*x^6 - 8*x^7 + 9*x^8)/((1 - 3*x - 3*x^2 - 6*x^3 - 2*x^4 + 3*x^5 + 2*x^6 - x^7)*(1 + x + x^2)) + O(x^30)) \\ Andrew Howroyd, Aug 10 2017

Crossrefs

Cf. A284700.

Sequence in context: A263218 A189305 A043011 * A138156 A280392 A192809

Adjacent sequences: A290695 A290696 A290697 * A290699 A290700 A290701

Keyword

nonn

Author

Eric W. Weisstein, Aug 09 2017

Extensions

a(1)-a(2) and terms a(7) and beyond from Andrew Howroyd, Aug 10 2017

Status

approved