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

1,1

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).

Links

Table of n, a(n) for n=1..52.

Project Euler, Problem 256: Tatami-Free Rooms

Formula

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

Example

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.

Crossrefs

Cf. A068920.

Sequence in context: A345487 A114838 A036191 * A295807 A136117 A224553

Adjacent sequences: A165629 A165630 A165631 * A165633 A165634 A165635

Keyword

nonn

Author

M. F. Hasler, Sep 26 2009

Status

approved