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

1,14

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.

Links

Table of n, a(n) for n=1..105.

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

Formula

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

Example

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.

Crossrefs

Cf. A068920.

Sequence in context: A043280 A030379 A030392 * A349236 A117456 A030621

Adjacent sequences: A165630 A165631 A165632 * A165634 A165635 A165636

Keyword

nonn

Author

M. F. Hasler, Sep 26 2009

Status

approved