#StackBounty: #code-challenge #sequence #geometry #polyomino Counting generalized polyominoes

Bounty: 100

This challenge will have you count pseudo-polyforms on the snub square tiling.

I think that this sequence does not yet exist on the OEIS, so this challenge exists to compute as many terms as possible for this sequence.

Definitions

The snub square tiling is a semiregular tiling of the plane that consists of equilateral triangles and squares.

snub square tiling

A pseudo-polyform on the snub square tiling is a plane figure constructed by joining together these triangles and squares along their shared sides, analogous to a polyomino. Here is an example of a six-cell and an eight-cell pseudo-polyform:

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Examples

For n = 1 there are two 1-cell pseudo-polyforms, namely the square and the triangle:

For n = 2 there are two 2-cell pseudo-polyforms, namely a square with a triangle and two triangles.

For n = 3 there are four 3-cell pseudo-polyforms.

Challenge

The goal of this challenge is to compute as many terms as possible in this sequence, which begins 2, 2, 4, ... and where the n-th term is the number of n-cell pseudo-polyforms up to rotation and reflection.

Run your code for as long as you’d like. The winner of this challenge will be the user who posts the most terms of the sequence, along with their code. If two users post the same number of terms, then whoever posts their last term earliest wins.

(Once there are enough known terms to prove that this sequence does not already exist in the OEIS, I’ll create an entry in the OEIS and list the contributor as a co-author if he or she desires.)


Get this bounty!!!

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