cp's OEIS Frontend

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

%I A165633 #4 Jul 14 2012 11:32:31
%S A165633 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,
%T A165633 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,
%U A165633 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
%N A165633 Number of tatami-free rooms of given size A165632(n).
%C A165633 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.
%H A165633 Project Euler, <a href="http://projecteuler.net/index.php?section=problems&amp;id=256">Problem 256: Tatami-Free Rooms</a>, Sept. 2009.
%F A165633 A165633 = #{ {r,c} | rc = A165632(n) }.
%e A165633 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.
%e A165633 a(237)=5 because there are 5 different rectangles of size A165632(237)=1320 which cannot be tiled in the given way.
%Y A165633 Cf. A068920.
%K A165633 nonn
%O A165633 1,14
%A A165633 _M. F. Hasler_, Sep 26 2009