A265030 Numerator of Kirchhoff index of ladder graph L_n.

1, 5, 71, 214, 11725, 6031, 415177, 140972, 1305393, 14793725, 289997917, 57882242, 6527639365, 7542845429, 1833039251, 19332937048, 2753465251825, 337099968813, 53020154848357, 28728290846950, 329717936541119, 1057437743438813, 17980324175708377, 1583743732945924

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Z. Cinkir, Effective Resistances, Kirchhoff index and Admissible Invariants of Ladder Graphs, arXiv preprint arXiv:1503.06353 [math.CO], 2015.

Formula

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

Example

1, 5, 71/5, 214/7, 11725/209, 6031/65, 415177/2911, 140972/679, ...

Mathematica

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 *)

Crossrefs

Cf. A265031.

Sequence in context: A141852 A142052 A139930 * A295332 A123077 A171554

Adjacent sequences: A265027 A265028 A265029 * A265031 A265032 A265033

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 02 2015

Extensions

a(5) corrected by Altug Alkan, Dec 02 2015

More terms from Robert G. Wilson v, Dec 02 2015

Status

approved