OFFSET
0,4
COMMENTS
By "L-connected" we mean that every pair of cells in the polyomino can be connected by a chain of cells in the polyomino, consisting of a vertical chain and a horizontal chain that share one of their end cells.
We consider the empty polyomino, or "nullomino" to be L-connected because there are no pairs of cells, so the universal quantifier in the definition is trivially satisfied.
The entries through n = 6 were hand-counted by Allan C. Wechsler, and John Mason confirmed those entries and extended the data through n = 18.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Andrew Howroyd, Formula and PARI program, 2023.
Wikipedia, Polyomino
EXAMPLE
For n = 4 the 4 solutions are the straight tetromino, the L tetromino, the T tetromino, and the square tetromino. The skew or S tetromino is not L-connected, because there is no qualifying path between the two most distant cells.
PROG
(PARI) seq(40) \\ See Links - Andrew Howroyd, Jan 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Allan C. Wechsler and John Mason, Jan 23 2023
EXTENSIONS
Terms a(19) and beyond from Andrew Howroyd, Jan 24 2023
STATUS
approved