OFFSET
2,3
COMMENTS
a(8) <= 54, a(9) <= 160.
Apparently, a(n) is close to A365621(n+1) for n <= 8. Is this just a coincidence?
EXAMPLE
For n <= 4, all polyominoes with n-1 cells are needed to obtain all polyominoes with n cells by adding one cell, so a(n) = A000105(n-1).
For n = 5, all but the square tetromino are needed to obtain all pentominoes, so a(5) = A000105(4)-1 = 4.
For n = 6, there are 5 different sets of a(6) = 8 pentominoes that are sufficient to obtain all hexominoes. One of these sets consists of the I, L, N, P, U, V, W, and Y pentominoes. The X pentomino is the only pentomino that does not appear in any of these sets. The I, L, N, and W pentominoes are needed in all such sets.
For n = 7, there are 8 different sets of a(7) = 19 hexominoes that are sufficient to obtain all heptominoes. 14 hexominoes appear in all these sets, 10 appear in none of them.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Nov 18 2023
STATUS
approved