A095968 Number of tilings of an n X n section of the square lattice with "ribbon tiles". A ribbon tile is a polyomino which has at most one square on each diagonal running from northwest to southeast.

1, 1, 9, 576, 254016, 768398400, 15933509222400, 2264613732270489600, 2206116494952210583142400, 14730363379319627387434460774400, 674138394386323094302100270094090240000, 211463408638810917171920642017084851413975040000

Offset: 0

Author

Isabel C. Lugo (izzycat(AT)gmail.com), Jul 15 2004

Keywords

• easy
• nonn

Comments

log G(n) is asymptotically equal to 2n^2 log phi.

Partial products of A049684. - R. J. Mathar, Oct 30 2010

Examples

			a(2) = 9 since there are nine tilings of the two X two square with ribbon tiles - the tiling with four monominoes, the four tilings with one domino and two monominoes, the two tilings with two dominoes and two tilings with a tromino and a monomino (the monomino is in either the SE or NW corner).
		

References

• R. P. Stanley and W. Y. C. Chen, Problem 10199, American Mathematical Monthly, Vol. 101 (1994), pp. 278-279.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..40
• I. C. Lugo, On some tilings with ribbon tiles.

Programs

Maple

with(combinat); F := fibonacci; seq(product(F(2*j)^2, j=0..n), n=1..12);

Formula

a(n) = prod(F(2*i)^2, i=1..n) where F(i) are the Fibonacci numbers.

Extensions

Corrected factor 2 in the formula - R. J. Mathar, Oct 29 2010