|
%I #21 Dec 04 2015 23:17:56
%S 1,1,5,7,209,65,2911,679,4505,37829,564719,87815,7865521,7338631,
%T 1460701,12776743,1525870529,158184065,21252634831,9914489123,
%U 98670339035,276182038859,4122901604639,320559963815
%N Denominator of Kirchhoff index of ladder graph L_n.
%H Z. Cinkir, <a href="http://arxiv.org/abs/1503.06353">Effective Resistances, Kirchhoff index and Admissible Invariants of Ladder Graphs</a>, arXiv preprint arXiv:1503.06353 [math.CO], 2015.
%F a(n) = denominator of k(n) = (1/3)*n^2*(n-sqrt(3)/tanh(n*log(2-sqrt(3)))). k(n) is also equal to n*(n^2-1)/3 + n*sum(k=0, n-1, 1/(1 + 2*sin(Pi*k/(2*n))^2)). - _Altug Alkan_, Dec 02 2015
%e 1, 5, 71/5, 214/7, 11725/209, 6031/65, 415177/2911, 140972/679, ...
%t f[n_] := Denominator@ Simplify[(1/3)*n^2*(n - Sqrt[3]/Tanh[n*Log[2 - Sqrt[3]]])]; Array[f, 45] (* _Robert G. Wilson v_, Dec 02 2015 *)
%Y Cf. A265030.
%K nonn,frac
%O 1,3
%A _N. J. A. Sloane_, Dec 02 2015
%E a(5) corrected by _Altug Alkan_, Dec 02 2015
%E More terms from _Robert G. Wilson v_, Dec 02 2015
|
