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A151525 Number of poly-IH64-tiles (holes allowed) with n cells. 4
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 (list; graph; refs; listen; history; text; internal format)



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.


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


Table of n, a(n) for n=1..28.

Jean-François Alcover, Mathematica program

Wikipedia, Polyomino


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


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




Ed Pegg Jr, May 13 2009


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

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



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Last modified December 1 14:02 EST 2021. Contains 349429 sequences. (Running on oeis4.)