A007239 Energy function for hexagonal lattice.

3, 6, 12, 24, 54, 138, 378, 1080, 3186, 9642, 29784, 93552, 297966, 960294, 3126408, 10268688, 33989388, 113277582, 379833906, 1280618784, 4339003044, 14767407522, 50464951224, 173099580168, 595786322292, 2057106617226, 7123467773790, 24734460619704

Offset: 1

Author

Simon Plouffe

Keywords

• nonn

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

References

• C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 386.
• 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)
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
• M. F. Sykes, Some counting theorems in the theory of the Ising problem and the excluded volume problem, J. Math. Phys., 2 (1961), 52-62.

Crossrefs

Cf. A002908.

Formula

See Eq. (32) of Sykes for the g.f. U(v). - Andrey Zabolotskiy, Feb 14 2022

Extensions

Terms a(21) and beyond from Andrey Zabolotskiy, Feb 14 2022