A007206 Magnetization for honeycomb lattice.

1, 0, 0, -2, -6, -18, -54, -168, -534, -1732, -5706, -19038, -64176, -218190, -747180, -2574488, -8918070, -31036560, -108457488, -380390574, -1338495492, -4723664566, -16714545822, -59286878556, -210755970528, -750721297056, -2679075662922, -9577156141654, -34290858526926, -122959225609518

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

References

• C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
• Shigeo Naya, On the Spontaneous Magnetizations of Honeycomb and Kagomé Ising Lattices, Progress of Theoretical Physics, 11 (1954), 53-62.

Crossrefs

Cf. A002928, A007207.

Programs

Mathematica

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 *)

Formula

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

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

Extensions

Offset changed, signs of terms changed, and more terms added by Andrey Zabolotskiy, Jun 01 2022