%I #9 Dec 16 2013 08:03:08
%S 1,1,9,576,254016,768398400,15933509222400,2264613732270489600,
%T 2206116494952210583142400,14730363379319627387434460774400,
%U 674138394386323094302100270094090240000,211463408638810917171920642017084851413975040000
%N 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.
%C log G(n) is asymptotically equal to 2n^2 log phi.
%C Partial products of A049684.  _R. J. Mathar_, Oct 30 2010
%D R. P. Stanley and W. Y. C. Chen, Problem 10199, American Mathematical Monthly, Vol. 101 (1994), pp. 278279.
%H Alois P. Heinz, <a href="/A095968/b095968.txt">Table of n, a(n) for n = 0..40</a>
%H I. C. Lugo, <a href="http://www.izzycat.org/math/index.php?p=51">On some tilings with ribbon tiles</a>.
%F a(n) = prod(F(2*i)^2, i=1..n) where F(i) are the Fibonacci numbers.
%e 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).
%p with(combinat); F := fibonacci; seq(product(F(2*j)^2, j=0..n), n=1..12);
%K easy,nonn
%O 0,3
%A Isabel C. Lugo (izzycat(AT)gmail.com), Jul 15 2004
%E Corrected factor 2 in the formula  _R. J. Mathar_, Oct 29 2010
