A165764 Smallest size of which there are n tatami-free rooms.

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

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, Sep 2009.

Formula

a(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

Cf. A068920, A165632, A165633, A165765.

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