

A182645


Number of polyIH68tiles (holes allowed) with n cells.


4



1, 1, 4, 10, 34, 110, 388, 1369, 4982, 18246, 67727, 253014, 952275, 3602743, 13698525, 52297602, 200402285, 770414503, 2970385477, 11482405741, 44491816601, 172766346508, 672186393972, 2619994613794, 10228901862928, 39996339056273, 156612019296546, 614044339256951
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OFFSET

1,3


COMMENTS

Equivalently, polyominoes where two polyominoes are considered the same if and only if they are related by a translation or a reflection in a NESW diagonal line.


REFERENCES

Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 6.2 and 9.4.


LINKS

Table of n, a(n) for n=1..28.
JeanFrançois Alcover, Mathematica program
Wikipedia, Polyomino


FORMULA

a(n) = 4*A006749(n) + 2*A006746(n) + 3*A006748(n) + 2*A006747(n) + A056877(n) + 2*A056878(n) + A144553(n) + A142886(n).  Andrew Howroyd, Dec 04 2018


CROSSREFS

Polyominoes by group of symmetries relating shapes considered the same: A000105 (all symmetries), A001168 (translations only), A000988 (rotations and translations), A056780 (horizontal and vertical reflections, rotations of order 2 and translations), A056783 (reflections in either diagonal, rotations of order 2 and translations), A151522 (rotations of order 2 and translations), A151525 (reflections in a horizontal line and translations), A182645 (reflections in a NESW diagonal line and translations)
Sequence in context: A156700 A274479 A231524 * A006343 A149173 A149174
Adjacent sequences: A182642 A182643 A182644 * A182646 A182647 A182648


KEYWORD

nonn


AUTHOR

Joseph Myers, Nov 24 2010


EXTENSIONS

a(19)a(28) from Andrew Howroyd, Dec 04 2018


STATUS

approved



