A341630 Number of fixed polyiamonds of area n without holes.

2, 3, 6, 14, 36, 94, 250, 675, 1832, 5005, 13746, 37901, 104902, 291312, 811346, 2265905, 6343854, 17801383, 50057400, 141034248, 398070362, 1125426581, 3186725646, 9036406687, 25658313188, 72946289247, 207628101578, 591622990214, 1687527542874, 4818113792640

Offset: 1

Author

Andrey Zabolotskiy, Feb 16 2021

Keywords

• nonn

Comments

Equivalently, closed self-avoiding paths on the hexagonal net, where rotations and reflections of the whole path are not allowed and there is no selected starting point, with enclosed area n.

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 1..60 (from Iwan Jensen's table)
• Anthony J. Guttmann, editor, Polygons, Polyominoes and Polycubes, LNP 775, Springer, 2009. See Table 16.8 "Triangular lattice SAP by area" on p. 476 with reference "Iwan Jensen, Unpublished".
• Index entries for sequences related to A2 = hexagonal = triangular lattice

Crossrefs

Cf. A001420 (polyiamonds with holes allowed; first deviates at n=9), A036418 (polyiamonds with given perimeter, i.e. paths with given length), A070765 (free polyiamonds, i.e. reduced for symmetry: rotations and reflections are allowed), A006724 (analog for square lattice).