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A165764 Smallest size of which there are n tatami-free rooms. 2
70, 198, 336, 504, 1320, 1440, 3696, 3360, 5040, 8400, 6720, 10080, 16632, 16800, 18480, 20160, 15120, 33264, 37800, 30240, 45360, 73920, 60480, 65520, 85680, 55440, 124740, 142560, 138600, 151200, 131040, 180180, 257040, 110880, 166320 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A tatami-free room is a rectangle of even size that allows no 1x2 domino tiling satisfying the tatami rule, i.e. such that there is no point in which 4 tiles meet.

a(n)=A165632(A165765(n)) where A165765(n) is the least index for which A165633(A165765(n))=n.

LINKS

Table of n, a(n) for n=1..35.

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

FORMULA

A165764(n) = A165632(A165765(n)) = min { r*c in 2Z | #{{r,c} | A068920(r,c)=0 } = n }

EXAMPLE

The smallest tatami-free room is of size 7x10, and all other rectangles of this size allow for a tatami tiling, thus a(1) = 70.

a(5)=1320 is the smallest size of which there are exactly 5 tatami-free rooms, namely 20x66, 22x60, 24x55, 30x44 and 33x40.

CROSSREFS

Sequence in context: A278782 A154361 A165762 * A153669 A235310 A235303

Adjacent sequences:  A165761 A165762 A165763 * A165765 A165766 A165767

KEYWORD

nonn

AUTHOR

M. F. Hasler, Sep 26 2009

STATUS

approved

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Last modified September 24 19:49 EDT 2022. Contains 356949 sequences. (Running on oeis4.)