cp's OEIS Frontend

A002978 Low-temperature series in y = exp(2J/kT) for antiferromagnetic susceptibility for the Ising model on honeycomb structure.

%I A002978 M3189 #22 Mar 03 2021 09:37:31
%S A002978 0,0,4,0,12,8,48,96,320,888,2748,8384,26340,83568,268864,873648,
%T A002978 2865216,9470784,31525524,105594912,355673804,1204059144,4094727168,
%U A002978 13983145888,47932777680,164881688088,568990371212,1969356192624,6834965581764,23782468159920
%N A002978 Low-temperature series in y = exp(2J/kT) for antiferromagnetic susceptibility for the Ising model on honeycomb structure.
%C A002978 Previous name was: Susceptibility series for honeycomb.
%D A002978 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002978 Y. Chan, A. J. Guttmann, B. G. Nickel, J. H. H. Perk, <a href="https://doi.org/10.1007/s10955-011-0212-0">The Ising Susceptibility Scaling Function</a>, J Stat Phys 145 (2011), 549-590; arXiv:<a href="https://arxiv.org/abs/1012.5272">1012.5272</a> [cond-mat.stat-mech], 2010-2020. Gives 641 term in the file Honeycomb_y641_af_.txt.
%H A002978 M. F. Sykes and M. E. Fisher, <a href="https://doi.org/10.1016/0031-8914(62)90080-0">Antiferromagnetic susceptibility of the plane square and honeycomb Ising lattices</a>, Physica, 28 (1962), 919-938.
%H A002978 M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, <a href="https://doi.org/10.1088/0305-4470/5/5/004">High temperature series for the susceptibility of the Ising model, I. Two dimensional lattices</a>, J. Phys. A 5 (1972) 624-639.
%F A002978 From _Andrey Zabolotskiy_, Mar 03 2021: (Start)
%F A002978 a(n) = 4*A007214(n-3).
%F A002978 G.f.: 8*t(u(y)) - 4*h(y), where t(u) is the g.f. of A047709, h(y) is the g.f. of A002912, and u(y) = y/(1-y+y^2) [Sykes & Fisher, p. 934-935]. (End)
%Y A002978 Cf. A002910, A002912, A007214-A007218, A057391, A057395, A047709, A128834.
%K A002978 nonn,nice
%O A002978 1,3
%A A002978 _N. J. A. Sloane_
%E A002978 New name from and more terms from Chan et al added by _Andrey Zabolotskiy_, Mar 03 2021