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A181369
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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.
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1
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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
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2,2
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COMMENTS
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f. = z^2*(1-z)^6/(1-4z+2z^2)^2.
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EXAMPLE
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a(3)=2 because the L-convex polyominoes of semiperimeter 3 are the horizontal and the vertical dominoes, each containing one maximal rectangle.
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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