A020866 Number of strong edge-subgraphs in Moebius ladder M_n.

41, 265, 1697, 10897, 69941, 448945, 2881697, 18497137, 118730021, 762108145, 4891844657, 31399932337, 201550911701, 1293721577905, 8304182337857, 53303156937457, 342144045482501, 2196165379031665, 14096818096762577, 90485116626705457, 580808823292457141

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Also known as the number of edge covers in the Moebius ladder M_n. - Eric W. Weisstein, Mar 31 2017

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.
• Index entries for linear recurrences with constant coefficients, signature (5,9,1,-2).

Programs

Maple

with(combinat): lucas:= n->fibonacci(n+1)+fibonacci(n-1):seq(lucas(2*n)+coeff(convert(series(x*(4+2*x+3*x^2-4*x^3+x^4)/((1+x)*(1-3*x+x^2)*(1-6*x-3*x^2+2*x^3)),x,50),polynom),x,n),n=2..25); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005

Mathematica

Table[RootSum[2 - 3 # - 6 #^2 + #^3 &, #^n &] - (-1)^n, {n, 2, 20}] (* Eric W. Weisstein, Mar 31 2017 *)
LinearRecurrence[{5, 9, 1, -2}, {41, 265, 1697, 10897}, 20] (* Eric W. Weisstein, Mar 31 2017 *)

PARI

Vec(-x^2*(14*x^3-3*x^2-60*x-41)/((x+1)*(2*x^3-3*x^2-6*x+1)) + O(x^30)) \\ Colin Barker, Aug 02 2015

Formula

a(n) = Lucas(2n) + [x^n] x(4+2x+3x^2-4x^3+x^4)/((1+x)(1-3x+x^2)(1-6x-3x^2+2x^3)); a(n) ~ (6.4188)^n + (-0.8056)^n + (0.3867)^n - (- 1)^n (Th. 3.2.). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005

From R. J. Mathar, Feb 06 2010: (Start)

a(n) = 5*a(n-1) + 9*a(n-2) + a(n-3) - 2*a(n-4).

G.f.: -x^2*(-41-60*x-3*x^2+14*x^3)/ ((1+x) * (2*x^3-3*x^2-6*x+1)). (End)

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005