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A360055
Number of L-connected free polyominoes with n cells (see comments for definition).
2
1, 1, 1, 2, 4, 7, 14, 24, 48, 83, 155, 265, 472, 793, 1356, 2235, 3700, 5977, 9636, 15262, 24068, 37439, 57920, 88628, 134838, 203264, 304688, 453126, 670238, 984556, 1438878, 2089996, 3021162, 4343229, 6215668, 8851151, 12550775, 17716075, 24907961, 34873541, 48644474
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, 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
Main entry at A000105; see the cross-references there.
Cf. A126764 (the fixed case).
Sequence in context: A056180 A000076 A217730 * A347760 A218576 A054169
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