The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%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. 278-279.

%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 15 03:12 EDT 2024. Contains 373402 sequences. (Running on oeis4.)