A151525 Number of poly-IH64-tiles (holes allowed) with n cells.

1, 2, 4, 12, 35, 116, 392, 1390, 4998, 18321, 67791, 253288, 952527, 3603761, 13699516, 52301427, 200406183, 770429000, 2970400815, 11482461055, 44491876993, 172766558719, 672186631950, 2619995431640, 10228902801505, 39996342220199, 156612023001490, 614044351536722

Offset

1,2

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 horizontal line. Formerly described as one-sided polyrects, but that is A151522.

References

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

Links

John Mason, Table of n, a(n) for n = 1..50

Jean-François Alcover, Mathematica program

Wikipedia, Polyomino

Formula

a(n) = 4*A006749(n) + 3*A006746(n) + 2*A006748(n) + 2*A006747(n) + 2*A056877(n) + 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 NE-SW diagonal line and translations)

Sequence in context: A209027 A069727 A148204 * A148205 A019447 A148206

Adjacent sequences: A151522 A151523 A151524 * A151526 A151527 A151528

Keyword

nonn

Author

Ed Pegg Jr, May 13 2009

Extensions

Edited and a(13)-a(18) by Joseph Myers, Nov 24 2010

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

Status

approved