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%I A047712 #37 Jan 19 2023 03:27:43
%S A047712 6,24,132,816,5448,38808,290568,2255232,17981532,146428728,1213014960,
%T A047712 10192820592,86687830596,744919762584
%N A047712 High-temperature coefficients for internal energy for spin-1/2 Ising model on f.c.c. lattice.
%H A047712 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.
%H A047712 S. McKenzie, <a href="https://doi.org/10.1088/0305-4470/16/12/033">Extended high-temperature series expansions for the spin-s Ising model</a>, J. Phys. A: Math. Gen., 16 (1983), 2875-2880. See table 1, column c(n); divide by 2 to get a(n).
%H A047712 M. F. Sykes, J. L. Martin and D. L. Hunter, <a href="https://doi.org/10.1088/0370-1328/91/3/320">Specific heat of a three-dimensional Ising ferromagnet above the Curie temperature</a>, Proc. Phys. Soc., 91 (1967), 671-677.
%H A047712 <a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>
%F A047712 G.f. 6*v + 24*v^2 + 132*v^3 + 816*v^4 ... = v*q/2 + (1-v^2) * f'(v) / f(v), where f(v) = 1 + 8*v^3 + 33*v^4 + ... is the g.f. of A001407 and q = 12 is the number of nearest neighbors. - _Andrey Zabolotskiy_, Feb 14 2022
%Y A047712 Cf. A010571 (cubic), A047711 (b.c.c.), A001407 (partition function), A002918 (specific heat).
%K A047712 nonn,more
%O A047712 1,1
%A A047712 _N. J. A. Sloane_
%E A047712 a(9)-a(11) from Sykes, Martin & Hunter added by _Andrey Zabolotskiy_, Feb 05 2022
%E A047712 Name clarified and a(12)-a(13) added by _Andrey Zabolotskiy_, Feb 14 2022
%E A047712 a(14) from McKenzie added by _Andrey Zabolotskiy_, Jan 18 2023

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