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 A265031 Denominator of Kirchhoff index of ladder graph L_n. 1
 1, 1, 5, 7, 209, 65, 2911, 679, 4505, 37829, 564719, 87815, 7865521, 7338631, 1460701, 12776743, 1525870529, 158184065, 21252634831, 9914489123, 98670339035, 276182038859, 4122901604639, 320559963815 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 15 03:00 EDT 2024. Contains 375931 sequences. (Running on oeis4.)