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Magnetization for square lattice.
(Formerly M1853 N0733)
5

%I M1853 N0733 #28 Apr 27 2024 14:26:18

%S 1,0,-2,-8,-34,-152,-714,-3472,-17318,-88048,-454378,-2373048,

%T -12515634,-66551016,-356345666,-1919453984,-10392792766,-56527200992,

%U -308691183938,-1691769619240,-9301374102034

%N Magnetization for square lattice.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D J. M. Yeomans, Statistical mechanics of phase transitions, Oxford Univ. Press, 1992, p. 93.

%H C. Domb, <a href="/A007239/a007239.pdf">Ising model</a>, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)

%H David Park, <a href="https://doi.org/10.1016/S0031-8914(56)90050-7">A summation method for crystal statistics</a>, Physica 22 (1956), 932-940.

%F n*a(n) + 6*(-n+1)*a(n-1) + 4*a(n-2) + 6*(n-3)*a(n-3) + (-n+4)*a(n-4) = 0. - _R. J. Mathar_, Mar 08 2013

%F a(n) ~ -Gamma(1/8) * (1 + sqrt(2))^(2*n - 1/2) / (Pi * 2^(57/16) * n^(9/8)). - _Vaclav Kotesovec_, Apr 27 2024

%p series((1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2),x,40).

%t CoefficientList[Series[(1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 27 2024 *)

%Y Cf. other structures: A007206, A007207, A002929, A002930, A003193, A003196.

%Y Cf. higher spins: A010102, A010105/A030120, A010103, A010106/A030121, A010104.

%Y Cf. Potts model: A057374, A057378.

%Y Cf. A002927 (susceptibility).

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_, _Simon Plouffe_