A265030 - OEIS

%I #19 Dec 11 2015 09:00:31

%S 1,5,71,214,11725,6031,415177,140972,1305393,14793725,289997917,

%T 57882242,6527639365,7542845429,1833039251,19332937048,2753465251825,

%U 337099968813,53020154848357,28728290846950,329717936541119,1057437743438813,17980324175708377,1583743732945924

%N Numerator 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) = numerator 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_] := Numerator@ Simplify[(1/3)*n^2*(n - Sqrt[3]/Tanh[n*Log[2 - Sqrt[3]]])]; Array[f, 24] (* _Robert G. Wilson v_, Dec 02 2015 *)

%Y Cf. A265031.

%K nonn,frac

%O 1,2

%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