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Number of counterclockwise n-step spirals on hexagonal lattice where turns of 2*Pi/3 are forbidden.
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%I #19 Oct 10 2019 03:56:35

%S 1,2,4,8,16,31,60,112,207,375,667,1173,2026,3466,5846,9770,16138,

%T 26441,42893,69073,110309,174972,275554,431286,670782,1037412,1595412,

%U 2440904,3715497,5628849,8487944,12743206,19050110,28362647,42060657,62137953,91461095,134144841,196071213

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

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

%C Corresponds to Model II of the Szekeres and Guttmann paper.

%H Sean A. Irvine, <a href="/A309982/b309982.txt">Table of n, a(n) for n = 1..58</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>

%H G. Szekeres and A. J. Guttmann, <a href="https://doi.org/10.1088/0305-4470/20/2/033">Spiral self-avoiding walks on the triangular lattice</a>, J. Phys. A 20 (1987), 481-493.

%Y Cf. A006776 (Model III).

%K nonn

%O 1,2

%A _Sean A. Irvine_, Aug 26 2019