A165633 Number of tatami-free rooms of given size A165632(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 4, 2, 1, 1, 1

Offset: 1

Author

M. F. Hasler, Sep 26 2009

Keywords

• nonn

Comments

Number of rectangles of size A165632(n) which cannot be tiled with tatamis of size 1x2 such that not more than 3 tatamis meet at any point.

Examples

			a(1)=1 because the rectangle of size 7x10 is the only one of size 70 that cannot be filled with 2x1 tiles without having 4 tiles meet in some point.
a(237)=5 because there are 5 different rectangles of size A165632(237)=1320 which cannot be tiled in the given way.
		

Links

• Project Euler, Problem 256: Tatami-Free Rooms, Sept. 2009.

Crossrefs

Cf. A068920.

Formula

A165633 = #{ {r,c} | rc = A165632(n) }.