The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A265030 Numerator of Kirchhoff index of ladder graph L_n. 1
 1, 5, 71, 214, 11725, 6031, 415177, 140972, 1305393, 14793725, 289997917, 57882242, 6527639365, 7542845429, 1833039251, 19332937048, 2753465251825, 337099968813, 53020154848357, 28728290846950, 329717936541119, 1057437743438813, 17980324175708377, 1583743732945924 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 03:24 EDT 2024. Contains 373432 sequences. (Running on oeis4.)