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.

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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

A056882 Number of n-celled polyominoes without holes, symmetric about diagonal 2.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 2, 3, 4, 4, 6, 7, 12, 12, 17, 18, 33, 34, 51, 52, 93, 100, 154, 152, 276, 300, 474, 460, 846, 929, 1491, 1431, 2667, 2956
Offset: 1

Views

Author

N. J. A. Sloane, Sep 03 2000

Keywords

Links

Crossrefs

Cf. A000104, A056878 (with holes allowed).

Extensions

a(29)-a(40) from John Mason, Oct 10 2022

A351159 Number of polyominoes of n cells with both diagonal symmetries, for which the 180-degree rotational symmetry has an axis that coincides with the center of a square, but without 90-degree rotational symmetry.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 3, 1, 6, 4, 9, 6, 20, 19, 32, 25, 64, 82, 114, 107, 217, 332, 397, 442, 751, 1316
Offset: 1

Views

Author

John Mason, Feb 03 2022

Keywords

Comments

This sequence enumerates a subset of the polyominoes enumerated by A056878.

Examples

			For a(7)=1, the heptomino with exactly fourfold symmetry and axes of symmetry parallel to the diagonals of the cells is composed of two 2 X 2 squares with one cell in common.

Crossrefs

Cf. A000105, A056878, A351160.

Formula

For odd n, a(n) = A056878(n); for even n, a(n) = A056878(n) - A351160(n/2).

A351160 Number of polyominoes of 2n cells with both diagonal symmetries, for which the 180-degree rotational symmetry has an axis that coincides with a vertex of a square, but without 90-degree rotational symmetry.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 4, 10, 14, 37, 55, 142, 208, 531, 792, 2015, 3029, 7621
Offset: 1

Views

Author

John Mason, Feb 03 2022

Keywords

Comments

This sequence enumerates a subset of the polyominoes enumerated by A056878.

Examples

			a(4)=1 because of:
    O
   OOO
  OOO
   O

Crossrefs

Cf. A000105, A056878, A351159.

Formula

a(n) = A056878(2*n) - A351159(2*n).

Extensions

a(17)-a(18) from John Mason, Dec 17 2024

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 21-25 of 25 results.

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

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