A309982 Number of counterclockwise n-step spirals on hexagonal lattice where turns of 2*Pi/3 are forbidden.

1, 2, 4, 8, 16, 31, 60, 112, 207, 375, 667, 1173, 2026, 3466, 5846, 9770, 16138, 26441, 42893, 69073, 110309, 174972, 275554, 431286, 670782, 1037412, 1595412, 2440904, 3715497, 5628849, 8487944, 12743206, 19050110, 28362647, 42060657, 62137953, 91461095, 134144841, 196071213

Offset

1,2

Comments

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

Corresponds to Model II of the Szekeres and Guttmann paper.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..58

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

G. Szekeres and A. J. Guttmann, Spiral self-avoiding walks on the triangular lattice, J. Phys. A 20 (1987), 481-493.

Crossrefs

Cf. A006776 (Model III).

Sequence in context: A299026 A007800 A362063 * A102726 A188900 A189075

Adjacent sequences: A309979 A309980 A309981 * A309983 A309984 A309985

Keyword

nonn

Author

Sean A. Irvine, Aug 26 2019

Status

approved