A369367 Number of free n-celled polyiamonds with the least number (A369366(n)) of inequivalent cells.

1, 1, 1, 3, 2, 1, 1, 1, 1, 4, 27, 1, 1, 6, 2, 1, 523, 1, 2, 17

Offset

1,4

Comments

From Peter Exley, Apr 08 2026: (Start)

A free polyiamond's cell orbits under its geometric automorphism group (a subgroup of D_6) partition the n cells into equivalence classes. a(n) counts how many free polyiamonds achieve the minimum orbit count A369366(n).

For most n, all minimizers share the same symmetry group order; the only exceptions in {1, ..., 20} are n = 4 and n = 10 where minimizers have mixed group orders. The spike values a(11) = 27 and a(17) = 523 occur when all minimizers have |G| = 2 (single reflection). Like the polyomino analog A367759 and the polyhex analog A369364, no closed form or recurrence is known; all three sequences fluctuate irregularly, with occasional large spikes (for example, A367759(18) = 33).

Computed by exhaustive enumeration of all free polyiamonds with Burnside orbit counting, verified by two independent methods. (End)

Links

Table of n, a(n) for n=1..20.

Peter Exley, Solver code, data, and figures, GitHub.

Index entries for sequences related to polyominoes.

Crossrefs

Cf. A000577, A367759, A369364, A369366.

Sequence in context: A090189 A227141 A284997 * A306709 A184532 A016557

Adjacent sequences: A369364 A369365 A369366 * A369368 A369369 A369370

Keyword

nonn,more

Author

Pontus von Brömssen, Jan 22 2024

Extensions

a(18) from John Mason, Sep 20 2024

a(19)-a(20) from Peter Exley, Apr 08 2026

Status

approved