

A181369


Number of maximal rectangles in all Lconvex polyominoes of semiperimeter n. An Lconvex 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 Lconvex polyomino P is a rectangle included in P that is maximal with respect to inclusion.


1



1, 2, 11, 44, 175, 682, 2617, 9920, 37232, 138600, 512412, 1883328, 6887056, 25074080, 90935120, 328658944, 1184206208, 4255136384, 15251769536, 54544092160, 194662703872, 693427554816, 2465864757504, 8754793857024
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OFFSET

2,2


COMMENTS

a(n) = Sum_{k>=1} A181368(n,k).


REFERENCES

G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of Lconvex polyominoes, European Journal of Combinatorics, 28, 2007, 17241741.
G. Castiglione and A. Restivo, Reconstruction of Lconvex polyominoes, Electronic Notes in Discrete Mathematics, Vol. 12, Elsevier Science, 2003.


LINKS

Table of n, a(n) for n=2..25.


FORMULA

G.f. = z^2*(1z)^6/(14z+2z^2)^2.


EXAMPLE

a(3)=2 because the Lconvex polyominoes of semiperimeter 3 are the horizontal and the vertical dominoes, each containing one maximal rectangle.


MAPLE

g := z^2*(1z)^6/(14*z+2*z^2)^2: gser := series(g, z = 0, 32): seq(coeff(gser, z, n), n = 2 .. 28);


CROSSREFS

Cf. A181368.
Sequence in context: A066058 A153440 A289645 * A037744 A037625 A181270
Adjacent sequences: A181366 A181367 A181368 * A181370 A181371 A181372


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Oct 17 2010


STATUS

approved



