A007239 Energy function for hexagonal lattice. (Formerly M2562)

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

1,1

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

Table of n, a(n) for n=1..28.

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.

Formula

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

Crossrefs

Cf. A002908.

Sequence in context: A084717 A102254 A278666 * A088970 A068425 A329355

Adjacent sequences: A007236 A007237 A007238 * A007240 A007241 A007242

Keyword

nonn

Author

Simon Plouffe

Extensions

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

Status

approved