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 A224850 Number T(n,k) of tilings of an n X k rectangle using integer sided square tiles reduced for symmetry, where the orbits under the symmetry group of the rectangle, D2, have 1 element; triangle T(n,k), k>=1, 0<=n
 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 3, 1, 1, 5, 2, 12, 6, 1, 1, 3, 3, 5, 7, 17, 1, 1, 8, 3, 25, 11, 106, 44 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS The triangle is: n\k  1   2   3   4   5   6   7   8 ... . 0    1   1   1   1   1   1   1   1 ... 1        1   1   1   1   1   1   1 ... 2            1   3   2   5   3   8 ... 3                1   2   2   3   3 ... 4                    3  12   5  25 ... 5                        6   7  11 ... 6                           17 106 ... 7                               44 ... It appears that sequence T(2,k) consists of 2 interspersed Fibonacci sequences. The diagonal T(n,n) is A006081. - M. F. Hasler, Jul 25 2013 LINKS Christopher Hunt Gribble, C++ program FORMULA T(n,k) + A224861(n,k) + A224867(n,k) = A227690(n,k). 1*T(n,k) + 2*A224861(n,k) + 4*A224867(n,k) = A219924(n,k). EXAMPLE T(3,5) = 2 because there are 2 different tilings of the 3 X 5 rectangle by integer sided squares, where any sequence of group D2 operations will only transform each tiling into itself.  Group D2 operations are: .   the identity operation .   rotation by 180 degrees .   reflection about a horizontal axis through the center .   reflection about a vertical axis through the center The tilings are: ._________.    ._________. |_|_|_|_|_|    |_|     |_| |_|_|_|_|_|    |_|     |_| |_|_|_|_|_|    |_|_____|_| CROSSREFS Cf. A219924, A224697, A227690. Sequence in context: A178252 A338199 A325498 * A269976 A132409 A030337 Adjacent sequences:  A224847 A224848 A224849 * A224851 A224852 A224853 KEYWORD nonn,tabl AUTHOR Christopher Hunt Gribble, Jul 22 2013 STATUS approved

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)