

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, 1, 9, 576, 254016, 768398400, 15933509222400, 2264613732270489600, 2206116494952210583142400, 14730363379319627387434460774400, 674138394386323094302100270094090240000, 211463408638810917171920642017084851413975040000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

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


REFERENCES

R. P. Stanley and W. Y. C. Chen, Problem 10199, American Mathematical Monthly, Vol. 101 (1994), pp. 278279.


LINKS



FORMULA

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


EXAMPLE

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).


MAPLE

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


CROSSREFS



KEYWORD

easy,nonn


AUTHOR

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


EXTENSIONS

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


STATUS

approved



