A049684 -id:A049684 - cp's OEIS frontend

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

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

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

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

			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).

R. P. Stanley and W. Y. C. Chen, Problem 10199, American Mathematical Monthly, Vol. 101 (1994), pp. 278-279.

Alois P. Heinz, Table of n, a(n) for n = 0..40
I. C. Lugo, On some tilings with ribbon tiles.

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

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

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

A288252 Positive integers n such that the Fibonacci (or Zeckendorf) representation of n^2 is a palindrome.

Original entry on oeis.org

1, 2, 3, 8, 21, 38, 55, 80, 144, 168, 174, 195, 314, 377, 682, 987, 2584, 6360, 6765, 12238, 13301, 17711, 34985, 46368, 54096, 66483, 87849, 121393, 219602, 317811, 684704, 832040, 1486717, 2178309, 3325460, 3940598, 5702887, 6151102, 10008701, 14930352

Offset: 1

Jeffrey Shallit, Jun 07 2017

nonn

The sequence is infinite because F(2n)^2 = A049684(n) has Fibonacci (or Zeckendorf) representation (1000)^(n-1) 1.

			38 is in the sequence because 38^2 = 1444 has Fibonacci representation 101000101000101, which is a palindrome.

Giovanni Resta, Table of n, a(n) for n = 1..60

Cf. A014417, which explains Fibonacci representation. Cf. A094202.

for n from 1 do
    zeck := A014417(n^2) ;
    if isA002113(zeck) then
        printf("%d,\n",n);
    end if;
end do: # R. J. Mathar, Jun 16 2017

a(35)-a(39) from Alois P. Heinz, Jun 14 2018

a(40) from Giovanni Resta, Jun 15 2018

cp's OEIS Frontend

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.

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