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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
OFFSET
1,3
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
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