A284869 Number of n-step 2-dimensional closed self-avoiding paths on triangular lattice, reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.

0, 0, 1, 1, 1, 4, 5, 16, 37, 120, 344, 1175, 3807, 13224, 45645, 161705, 575325, 2074088, 7521818, 27502445, 101134999, 374128188

Offset

1,6

Comments

Differs from A057729 beginning at n = 11, since that sequence includes triangular polyominoes with holes.

a(n) is the number of simply connected polyiamonds with perimeter n. - Walter Trump, Nov 29 2023

Links

Table of n, a(n) for n=1..22.

Rade Doroslovački, Ivan Stojmenović and Ratko Tošić, Generating and counting triangular systems, BIT Numerical Mathematics, 27 (1987), 18-24. See Table 1.

Hugo Pfoertner, Illustration of ratio A036418(n)/a(n) using Plot2.

Hugo Pfoertner, Illustration of polygons of perimeter <= 11.

Walter Trump, Self-avoiding closed walks on a triangular lattice

Crossrefs

Approaches (1/12)*A036418 for increasing n.

Cf. A057729, A258206, A266549, A316196.

Sequence in context: A196021 A064294 A352156 * A057729 A110278 A013628

Adjacent sequences: A284866 A284867 A284868 * A284870 A284871 A284872

Keyword

nonn,walk,more

Author

Luca Petrone, Apr 04 2017

Extensions

a(15) from Hugo Pfoertner, Jun 27 2018

a(16)-a(22) from Walter Trump, Nov 29 2023

Status

approved