A165633 - OEIS

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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

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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.