cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-26 of 26 results.

A182645 Number of poly-IH68-tiles (holes allowed) with n cells.

Original entry on oeis.org

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
Offset: 1

Views

Author

Joseph Myers, Nov 24 2010

Keywords

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

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)

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

Extensions

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

A056883 Number of n-celled rotationally symmetric polyominoes without holes.

Original entry on oeis.org

0, 0, 0, 1, 1, 5, 4, 18, 19, 72, 72, 268, 276, 1002, 1043, 3733, 3926, 14000, 14810, 52658, 55987, 199020, 212364, 754826, 807861, 2872926, 3082202, 10966333, 11789248, 41970489, 45198317, 160996986, 173640109, 618839771, 668316169, 2383000591, 2576516523, 9191269314, 9947949563, 35502661446
Offset: 1

Views

Author

N. J. A. Sloane, Sep 03 2000

Keywords

Comments

In other words, free unholey polyominoes with 180-degree rotational symmetry and no other. - John Mason, Oct 11 2022

Links

Crossrefs

Cf. A000104, A006747 (with holes allowed).

Extensions

a(29)-a(40) from John Mason, Oct 11 2022

A351191 Number of polyominoes of 4n cells with both horizontal and vertical symmetries, for which the 180-degree rotational symmetry has an axis that coincides with a vertex of a square of the underlying matrix, but without 90-degree rotational symmetry.

Original entry on oeis.org

0, 1, 2, 9, 29, 106, 372, 1356, 4928, 18200, 67541, 252847, 951615, 3602131, 13696141, 52295335, 200393559, 770406039, 2970353199, 11482373919, 44491696182, 172766226170, 672185941552, 2619994156474, 10228900153083, 39996337310835, 156612012801698
Offset: 1

Views

Author

John Mason, Feb 05 2022

Keywords

Comments

This sequence enumerates a subset of the polyominoes enumerated by A056877.

Examples

			a(2)=1 because of the 2 by 4 octomino.

Links

Crossrefs

Cf. A000105, A056877, A144553, A006747, A006746, A006749, A006748.

Formula

a(n)=A144553(n) + A056877(n) + 2 * A006747(n) + 2 * A006746(n) + 4 * A006749(n) + A006748(n).

A351615 Number of free polyominoes with n squares, having 180-degree rotational symmetry about the center of a square, and no other symmetry.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 4, 0, 19, 1, 73, 4, 283, 25, 1090, 106, 4183, 463, 16105, 1892, 62170, 7752, 240907, 31212, 936447, 125609, 3651618, 503165, 14277519, 2014826, 55961118, 8058790, 219813564, 32231897, 865091976, 128897247, 3410498446, 515554767, 13466262587, 2062445063, 53245595410, 8252868076, 210800433323
Offset: 1

Views

Author

John Mason, Feb 15 2022

Keywords

Comments

The sequence enumerates a subset of the polyominoes enumerated by A006747.

Examples

			a(5)=1 because of:
   OO
   O
  OO

Links

Crossrefs

Cf. A006747, A234008, A351616.

Extensions

More terms from John Mason, Apr 15 2023

A351616 Number of free polyominoes with 2n squares, having 180-degree rotational symmetry about a vertex of a square, and no other symmetry.

Original entry on oeis.org

0, 0, 1, 2, 12, 43, 174, 657, 2571, 9911, 38633, 150437, 588544, 2306204, 9061179, 35665587, 140648710, 555514177, 2197298561, 8702439446, 34506900216, 136972867380, 544237912916, 2164377093376, 8614630304437
Offset: 1

Views

Author

John Mason, Feb 15 2022

Keywords

Comments

The sequence enumerates a subset of the polyominoes enumerated by A006747.

Examples

			a(3)=1 because of:
   OOO
  OOO

Crossrefs

Cf. A006747, A234008, A351615.

Extensions

a(17)-a(25) from John Mason, Feb 26 2023

A176673 Partial sums of A001168.

Original entry on oeis.org

1, 3, 9, 28, 91, 307, 1067, 3792, 13702, 50148, 185416, 691277, 2595167, 9800041, 37194707, 141787644, 542583488, 2083404030, 8024142706, 30988922366, 119972435149, 465505007827, 1809877343351, 7049866113619, 27507668129630
Offset: 1

Views

Author

Jonathan Vos Post, Apr 23 2010

Keywords

Comments

Partial sums of number of fixed polyominoes with n cells, for n > 0.

Examples

			a(6) = 1 + 2 + 6 + 19 + 63 + 216 = 307.

Links

Crossrefs

Cf. A001168, A000105, A006746, A056877, A006748, A056878, A006747, A006749, A006762.

Formula

a(n) = Sum_{i=1..n} A001168(i).
Previous Showing 21-26 of 26 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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