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

0,3

Comments

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

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

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.

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

Sequence in context: A074731 A064560 A264121 * A233067 A067320 A061611

Adjacent sequences: A095965 A095966 A095967 * A095969 A095970 A095971

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