A284710 Number of maximal matchings in the n-Moebius ladder.

3, 3, 6, 23, 43, 102, 213, 447, 978, 2083, 4491, 9650, 20699, 44495, 95536, 205215, 440813, 946758, 2033611, 4367943, 9381882, 20151431, 43283105, 92967858, 199685543, 428904271, 921243300, 1978737343

Offset: 1

Author

Eric W. Weisstein, Apr 01 2017

Keywords

• nonn
• easy

Comments

Recurrence used to extrapolate to a(1) and a(2).

Links

• Eric Weisstein's World of Mathematics, Matching
• Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
• Eric Weisstein's World of Mathematics, Moebius Ladder
• Index entries for linear recurrences with constant coefficients, signature (1, 2, 1, -1, 2, 1, -1, -1).

Programs

Mathematica

LinearRecurrence[{1, 2, 1, -1, 2, 1, -1, -1}, {3, 3, 6, 23, 43, 102, 213, 447, 978}, 30]
Table[2 Cos[n Pi/3] + RootSum[-1 - 2 # - #^2 + #^3 &, #^n &] - RootSum[-1 + #^2 + #^3 &, #^n &], {n, 3, 20}]

Formula

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

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