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Polyiamondominoes

What are Polyiamondominoes?

Polyiamondominoes are a combination of Polyiamonds and Polyominoes. Essentially, k-iamonds||n-ominoes are the amount of distinct polyforms made with k triangles and n squares.

Enumeration

There are several ways to enumerate polyiamondominoes. The way I do it is using the differences. E.g:
Free polyiamondominoes with same amount of triangles and squares:
1, 15
Free polyiamondominoes with one more triangle than squares:
3
Free polyiamondominoes with one less triangle than squares:
3
Free polyiamondominoes with two more triangles than squares:
7
Free polyiamondominoes with two less triangles than squares:
11
etc.
If you'd like, you could help me calculate polyiamondominoes. I really need help, as you can see, there is a lack of terms.

List of Polyiamondominoes

Same

Moniamondmonominoes

There is one free moniamondmonomino, the house. It looks like a house and it has one-axis symmetry.

Diamondominoes

There are 15 free diamondominoes. Grouped in rows: First is both squares and triangles connected, second and third are squares connected, fourth is triangles connected and fifth is neither connected.
Triangles colored by symmetry, orange is asymmetric, purple is rotationally symmetric, red is two-axis symmetric, green is one-axis symetric.

References

Polyiamondominoes - Polypad
TriSquares - Google Docs
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