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A181369 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. 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 (list; graph; refs; listen; history; text; internal format)
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 L-convex polyominoes, European Journal of Combinatorics, 28, 2007, 1724-1741.

G. Castiglione and A. Restivo, Reconstruction of L-convex 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*(1-z)^6/(1-4z+2z^2)^2.

EXAMPLE

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

MAPLE

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);

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

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Last modified August 4 20:00 EDT 2020. Contains 336202 sequences. (Running on oeis4.)