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A182645 Number of poly-IH68-tiles (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 (list; graph; refs; listen; history; text; internal format)
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 NE-SW 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.

Jean-François 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 NE-SW 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

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)