id:A052270 - OEIS Search Results

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Consider a room of size r X s where rs = 2n and 1 <= r <= s; count ways to arrange n Tatami mats in room; a(n) = total number of ways for all choices of r and s. Two arrangements are considered the same if one is a rotation or reflection of the other.

+0
3

1, 2, 3, 4, 5, 9, 9, 14, 19, 27, 34, 56, 70, 105, 152, 218, 308, 466, 654, 966, 1407, 2052, 2979, 4399, 6378, 9361, 13697, 20051, 29308, 43035, 62885, 92204, 135053, 197871, 289775, 424891, 622199, 911988, 1336319, 1958344, 2869418, 4205888 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`Tatami mats are of size 1 X 2; at most 3 may meet at a point.`
	LINKS	`Dean Hickerson, Illustration of first few cases` `Dean Hickerson, Filling rectangular rooms with Tatami mats (Includes Mma program)` `Yasutoshi Kohmoto, Illustration of a(6) = 9`
	EXAMPLE	`For n = 3 there are 2 ways to cover a 2 X 3 room and 1 way to cover a 1 X 6 room, so a(3)=3:` `._____. ._____.` `\|___\| \| \| \| \| \| .___________.` `\|___\|_\| \|_\|_\|_\| \|___\|___\|___\|`
	CROSSREFS	`Cf. A067925 for total number of tilings, A068926 for table of number of incongruent tilings of an r X s room.` `Sequence in context: A072501 A092975 A046021 this_sequence A069117 A098464 A068586` `Adjacent sequences: A052267 A052268 A052269 this_sequence A052271 A052272 A052273`
	KEYWORD	`nonn,nice`
	AUTHOR	`Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)`
	EXTENSIONS	`Extended by Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 01 2002`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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