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%I #7 Jul 22 2022 12:28:21
%S 1,2,11,44,175,682,2617,9920,37232,138600,512412,1883328,6887056,
%T 25074080,90935120,328658944,1184206208,4255136384,15251769536,
%U 54544092160,194662703872,693427554816,2465864757504,8754793857024
%N Number of maximal rectangles in all L-convex polyominoes of semiperimeter n. An L-convex polyomino is a convex polyomino where any two cells can be connected by a path internal to the polyomino and which has at most 1 change of direction (i.e., one of the four orientations of the letter L). A maximal rectangle in an L-convex polyomino P is a rectangle included in P that is maximal with respect to inclusion.
%C a(n) = Sum_{k>=1} A181368(n,k).
%D G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European Journal of Combinatorics, 28, 2007, 1724-1741.
%D G. Castiglione and A. Restivo, Reconstruction of L-convex polyominoes, Electronic Notes in Discrete Mathematics, Vol. 12, Elsevier Science, 2003.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16,-4).
%F G.f. = z^2*(1-z)^6/(1-4z+2z^2)^2.
%e a(3)=2 because the L-convex polyominoes of semiperimeter 3 are the horizontal and the vertical dominoes, each containing one maximal rectangle.
%p g := z^2*(1-z)^6/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 32): seq(coeff(gser, z, n), n = 2 .. 28);
%Y Cf. A181368.
%K nonn,easy
%O 2,2
%A _Emeric Deutsch_, Oct 17 2010
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