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A360055 Number of L-connected free polyominoes with n cells (see comments for definition).

%I A360055 #38 Jan 28 2023 22:07:24
%S A360055 1,1,1,2,4,7,14,24,48,83,155,265,472,793,1356,2235,3700,5977,9636,
%T A360055 15262,24068,37439,57920,88628,134838,203264,304688,453126,670238,
%U A360055 984556,1438878,2089996,3021162,4343229,6215668,8851151,12550775,17716075,24907961,34873541,48644474
%N A360055 Number of L-connected free polyominoes with n cells (see comments for definition).
%C A360055 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.
%C A360055 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.
%C A360055 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.
%H A360055 Andrew Howroyd, <a href="/A360055/b360055.txt">Table of n, a(n) for n = 0..1000</a>
%H A360055 Andrew Howroyd, <a href="/A360055/a360055.txt">Formula and PARI program</a>, 2023.
%H A360055 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%e A360055 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.
%o A360055 (PARI) seq(40) \\ See Links - _Andrew Howroyd_, Jan 27 2023
%Y A360055 Main entry at A000105; see the cross-references there.
%Y A360055 Cf. A126764 (the fixed case).
%K A360055 nonn
%O A360055 0,4
%A A360055 _Allan C. Wechsler_ and _John Mason_, Jan 23 2023
%E A360055 Terms a(19) and beyond from _Andrew Howroyd_, Jan 24 2023