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