OFFSET

1,9

COMMENTS

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

EXAMPLE

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 ...

...

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

KEYWORD

AUTHOR

Christopher Hunt Gribble, Jul 22 2013

STATUS

approved