A265031 Denominator of Kirchhoff index of ladder graph L_n.

1, 1, 5, 7, 209, 65, 2911, 679, 4505, 37829, 564719, 87815, 7865521, 7338631, 1460701, 12776743, 1525870529, 158184065, 21252634831, 9914489123, 98670339035, 276182038859, 4122901604639, 320559963815

Offset

1,3

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) = 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

Example

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

Mathematica

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 *)

Crossrefs

Cf. A265030.

Sequence in context: A057177 A297535 A211769 * A229030 A229033 A187022

Adjacent sequences: A265028 A265029 A265030 * A265032 A265033 A265034

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