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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, 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 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.

Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).

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.