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

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.

Sequence in context: A066058 A153440 A289645 * A037744 A037625 A181270

Adjacent sequences: A181366 A181367 A181368 * A181370 A181371 A181372

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 17 2010

Status

approved