A068920 -id:A068920 - cp's OEIS frontend

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

M. F. Hasler, Sep 26 2009

nonn

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.

			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.

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

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

A165766 Number of tatami-free rooms of size 2n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0

Offset: 1

M. F. Hasler, Sep 26 2009

nonn

Number of pairs (r,c) such that r<=c, r*c=2n and A068920(r,c)=0.

A165632 lists twice the indices of nonzero terms, i.e. A165632 = { 2n | a(n)=0 }.

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

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A165766 Number of tatami-free rooms of size 2n.

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