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 (list; graph; refs; listen; history; internal format)

	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	`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 * A117456 A030621 A120336` `Adjacent sequences: A165630 A165631 A165632 * A165634 A165635 A165636`
	KEYWORD	`nonn`
	AUTHOR	`M. F. Hasler (www.univ-ag.fr/~mhasler), Sep 26 2009`

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Last modified February 15 02:50 EST 2012. Contains 205694 sequences.