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Magnetization for honeycomb lattice.
(Formerly M4124)
2

%I M4124 #18 Apr 27 2024 14:49:46

%S 1,0,0,-2,-6,-18,-54,-168,-534,-1732,-5706,-19038,-64176,-218190,

%T -747180,-2574488,-8918070,-31036560,-108457488,-380390574,

%U -1338495492,-4723664566,-16714545822,-59286878556,-210755970528,-750721297056,-2679075662922,-9577156141654,-34290858526926,-122959225609518

%N Magnetization for honeycomb lattice.

%D C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.

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

%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 Shigeo Naya, <a href="https://doi.org/10.1143/PTP.11.53">On the Spontaneous Magnetizations of Honeycomb and Kagomé Ising Lattices</a>, Progress of Theoretical Physics, 11 (1954), 53-62.

%F G.f.: (1 - 16 * z^3 * (1+z^3) / ((1-z)^3 * (1-z^2)^3))^(1/8) [Shigeo Naya]. - _Andrey Zabolotskiy_, Jun 01 2022

%F a(n) ~ -Gamma(1/8) * sqrt(sqrt(2) - 1) * (2 + sqrt(3))^n / (2^(27/8) * 3^(1/16) * Pi * n^(9/8)). - _Vaclav Kotesovec_, Apr 27 2024

%t CoefficientList[Series[(1 - 16 * x^3 * (1+x^3) / ((1-x)^3 * (1-x^2)^3))^(1/8), {x, 0, 30}], x] (* _Vaclav Kotesovec_, Apr 27 2024 *)

%Y Cf. A002928, A007207.

%K sign,easy

%O 0,4

%A _Simon Plouffe_

%E Offset changed, signs of terms changed, and more terms added by _Andrey Zabolotskiy_, Jun 01 2022