A010571 - OEIS

%I #24 Feb 15 2022 14:01:03

%S 3,12,120,1368,18300,268728,4179852,67767744,1133826324,19443072084,

%T 340085761968,6046276240668,108970501777080,1986820814551056,

%U 36587507853481908,679619087721892176,12720247240214281860,239685390231729125004,4543441582487318876664

%N High temperature expansion of -u/J in odd powers of v = tanh(J/kT), where u is energy per site of the spin-1/2 Ising model on cubic lattice with nearest-neighbor interaction J at temperature T.

%H M. E. Fisher and D. S. Gaunt, <a href="http://dx.doi.org/10.1103/PhysRev.133.A224">Ising model and self-avoiding walks on hypercubical lattices and high density expansions</a>, Phys. Rev., 133 (1964), A224-A239. See Table II for correct a(1)-a(6) but incorrect a(7).

%H M. E. Fisher and M. F. Sykes, <a href="https://doi.org/10.1016/0031-8914(62)90081-2">Antiferromagnetic susceptibilities of the simple cubic and body-centered cubic Ising lattices</a>, Physica, 28 (1962), 939-956.

%F Sum_{n>=1} a(n) * v^(2*n-1) = v*q/2 + (1-v^2) * f'(v) / f(v), where f(v) = Sum_{n>=0} A001393(n) * v^(2*n) and q = 6 is the number of nearest neighbors. - _Andrey Zabolotskiy_, Feb 14 2022

%Y Cf. A001393, A002908, A007239, A010572-A010574, A047711, A047712.

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_

%E New name from _Andrey Zabolotskiy_, Jan 14 2019

%E a(7) corrected and more terms added by _Andrey Zabolotskiy_, Feb 14 2022