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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.

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

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Last modified November 26 17:52 EST 2021. Contains 349343 sequences. (Running on oeis4.)