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

1,1

Comments

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

Links

Table of n, a(n) for n=1..28.

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).

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).

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}]

Crossrefs

Sequence in context: A025256 A052560 A147836 * A019235 A222020 A230253

Adjacent sequences: A284707 A284708 A284709 * A284711 A284712 A284713

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 01 2017

Status

approved