A020877 Number of matchings in Moebius ladder M_n.

10, 34, 106, 344, 1102, 3546, 11394, 36628, 117730, 378426, 1216378, 3909832, 12567446, 40395794, 129844994, 417363332, 1341539194, 4312135922, 13860583626, 44552347608, 143205490526, 460308235562, 1479577849602, 4755836293844, 15286778495570, 49136593930954

Offset

2,1

Comments

Also the Hosoya indices of the Moebius ladders. - Eric W. Weisstein, Jul 11 2011

Links

Colin Barker, Table of n, a(n) for n = 2..1000

J. P. McSorley, Counting structures in the Moebius ladder, Discrete Math., 184 (1998), 137-164.

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Moebius Ladder

Index entries for linear recurrences with constant coefficients, signature (2,4,0,-1).

Formula

G.f.: 2*x^2*(5+7*x-x^2-2*x^3)/((1+x)*(1-3*x-x^2+x^3)). - Emeric Deutsch, Dec 21 2004

a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4). - Eric W. Weisstein, Oct 03 2017 [Corrected by Altug Alkan, Apr 06 2018]

The McSorley reference gives the approximation a(n)~(3.2143)^n+(-0.6751)^n+(0.4608)^n-(-1)^n. - Emeric Deutsch, Dec 21 2004

Maple

G:=2*x^2*(5+7*x-x^2-2*x^3)/(1+x)/(1-3*x-x^2+x^3): Gser:=series(G, x=0, 29): seq(coeff(Gser, x^n), n=2..27); # Emeric Deutsch, Dec 21 2004

Mathematica

Table[RootSum[1 - # - 3 #^2 + #^3 &, #^n &] - (-1)^n, {n, 2, 20}] (* Eric W. Weisstein, Mar 31 2017 *)
LinearRecurrence[{2, 4, 0, -1}, {10, 34, 106, 344}, 20] (* Eric W. Weisstein, Mar 31 2017 *)
CoefficientList[Series[-2 (-5 - 7 x + x^2 + 2 x^3)/(1 - 2 x - 4 x^2 + x^4), {x, 0, 20}], x] (* Eric W. Weisstein, Oct 03 2017 *)

Prog

(PARI) Vec(-2*x^2*(2*x^3+x^2-7*x-5)/((x+1)*(x^3-x^2-3*x+1)) + O(x^50)) \\ Colin Barker, Aug 01 2015
(Magma) I:=[10, 34, 106, 344]; [n le 4 select I[n] else 2*Self(n-1)+4*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 07 2018

Crossrefs

Row sums of A302232.

Sequence in context: A297721 A019257 A288782 * A119171 A119229 A119227

Adjacent sequences: A020874 A020875 A020876 * A020878 A020879 A020880

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Dec 21 2004

Status

approved