A284701 Number of maximal matchings in the n-antiprism graph.

2, 6, 14, 46, 137, 354, 905, 2366, 6278, 16681, 44156, 116650, 308180, 814645, 2153984, 5695102, 15056494, 39804582, 105231559, 278204561, 735502187, 1944477640, 5140687360, 13590620330, 35930023287, 94989547620, 251127430313, 663914974741

Offset: 1

Author

Eric W. Weisstein, Apr 01 2017

Keywords

• nonn
• easy

Comments

Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, May 16 2017

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Antiprism Graph
• Eric Weisstein's World of Mathematics, Matching
• Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
• Index entries for linear recurrences with constant coefficients, signature (2,1,0,3,5,1,-2,-1).

Crossrefs

Cf. A284703, A284710, A192742, A284700.

Programs

Mathematica

LinearRecurrence[{2, 1, 0, 3, 5, 1, -2, -1}, {2, 6, 14, 46, 137, 354,
  905, 2366}, 20] (* Eric W. Weisstein, May 17 2017 *)
CoefficientList[Series[x*(-8*x^7-14*x^6+6*x^5+25*x^4+12*x^3+2*x+2)/(x^8 +2*x^7-x^6-5*x^5 -3*x^4-x^2-2*x+1), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)
Table[RootSum[1 + 2 # - #^2 - 5 #^3 - 3 #^4 - #^6 - 2 #^7 + #^8 &, #^n &], {n, 10}] (* Eric W. Weisstein, May 26 2017 *)

PARI

Vec((-8*x^7-14*x^6+6*x^5+25*x^4+12*x^3+2*x+2)/(x^8+2*x^7-x^6-5*x^5-3*x^4-x^2-2*x+1)+O(x^20)) \\ Andrew Howroyd, May 16 2017

Formula

From Andrew Howroyd, May 16 2017 (Start)

a(n) = 2*a(n-1) + a(n-2) + 3*a(n-4) + 5*a(n-5) + a(n-6) - 2*a(n-7) - a(n-8) for n>8.

G.f.: x*(-8*x^7 - 14*x^6 + 6*x^5 + 25*x^4 + 12*x^3 + 2*x + 2)/(x^8 + 2*x^7 - x^6 - 5*x^5 - 3*x^4 - x^2 - 2*x + 1). (End)

Extensions

a(1)-a(2) and a(16)-a(28) from Andrew Howroyd, May 16 2017