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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Row sums of A302232.

Programs

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

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 *)

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

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

Extensions

More terms from Emeric Deutsch, Dec 21 2004