OFFSET
0,3
LINKS
Hendrik A. Kramers and Gregory H. Wannier. Statistics of the two-dimensional ferromagnet. Part I. Phys. Rev. 60 (1941), 252-262.
Hendrik A. Kramers and Gregory H. Wannier. Statistics of the two-dimensional ferromagnet. Part II. Phys. Rev. 60 (1941), 263-276. See (41), p. 263.
Hendrik A. Kramers and Gregory H. Wannier, Extract from page 263 of Part II.
Gandhimohan M. Viswanathan, The hypergeometric series for the partition function of the 2D Ising model, J. Stat. Mech. (2015) P07004; arXiv:1411.2495 [cond-mat.stat-mech], 2014-2015.
Wikipedia, Square lattice Ising model.
FORMULA
a(n) / A370954(n) ~ c * 2^(2*n) / (n^3 * log(1 + sqrt(2))^(2*n)), where c = 0.15662885... - Vaclav Kotesovec, May 02 2024
MATHEMATICA
CoefficientList[With[{nmax = 7}, Exp[-Log[2]/2 + 1/(2 Pi) Integrate[Log[Cosh[2k]^2 + Sqrt[Sinh[2k]^4 + 1 - 2 Sinh[2k]^2 Cos[2\[Theta]] + O[k]^(2nmax+1)]], {\[Theta], 0, Pi}] + O[k]^(2nmax+1)]], k][[;; ;; 2]] // Numerator (* Andrey Zabolotskiy, Mar 10 2024 *)
CoefficientList[Cosh[2k] Exp[-x HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 2}, 16x] /. {x -> (Sinh[2k]/(2Cosh[2k]^2))^2}] + O[k]^32, k][[;; ;; 2]] // Numerator (* Andrey Zabolotskiy, Mar 13 2024, using the g. f. from Gandhimohan M. Viswanathan *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Mar 10 2024
EXTENSIONS
Terms a(5) and beyond from Andrey Zabolotskiy, Mar 10 2024
STATUS
approved