A165632 Sizes of tatami-free rooms.

70, 88, 96, 108, 126, 130, 140, 150, 154, 160, 176, 180, 192, 198, 204, 208, 216, 228, 234, 238, 240, 250, 252, 260, 266, 270, 280, 286, 294, 300, 304, 308, 320, 322, 330, 336, 340, 348, 352, 360, 368, 372, 374, 378, 384, 390, 396, 400, 408, 414, 416, 418

Offset: 1

Author

M. F. Hasler, Sep 26 2009

Keywords

• nonn

Comments

Even numbers s such that some rectangle of size s=r*c (r,c positive integers) cannot be tiled with tatamis of size 1x2 such that not more than 3 tatamis meet at any point.

The number of different rectangles of size a(n) which have this property is given in A165633(n).

Examples

			a(1)=70 because the rectangle of size 7x10 is the smallest that cannot be filled with 2x1 tiles without having 4 tiles meet in some point.
		

Links

• Project Euler, Problem 256: Tatami-Free Rooms

Crossrefs

Cf. A068920.

Formula

A165632 = { r*c in 2Z | A068920(r,c)=0 }