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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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).

A056879 Number of n-celled axially symmetric polyominoes without holes.

Original entry on oeis.org

0, 0, 0, 1, 2, 6, 9, 23, 37, 87, 138, 313, 510, 1130, 1859, 4070, 6786, 14750, 24811, 53715, 91096, 196769, 335815, 724470, 1243175, 2680212, 4619999, 9957652, 17231447, 37137177, 64480255, 138978282, 242011375, 521706359, 910817416, 1963885190, 3436463468, 7411495499, 12995261895, 28034824487
Offset: 1

Views

Author

N. J. A. Sloane, Sep 03 2000

Keywords

Links

Crossrefs

Cf. A000105, A000104, A006746.

Extensions

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

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).

A343562 The number of n-cell polyominoes with a line of symmetry parallel to the edges.

Original entry on oeis.org

1, 1, 1, 3, 4, 8, 12, 28, 44, 98, 157, 359, 583, 1324, 2183, 4961, 8263, 18729, 31477, 71231, 120605, 272380, 464188, 1046516, 1793505, 4036645, 6952368, 15623258, 27026985, 60645746, 105327495, 236021747, 411377265, 920654994, 1609862767, 3598552287
Offset: 1

Views

Author

R. J. Mathar, Sep 29 2021

Keywords

Comments

The polyominoes counted here may have additional symmetries (mirror axes along diagonals or rotational symmetries or two orthogonal mirror axes...). The mirror axes may run through cell edges or through cell centers.

Examples

			For n=4 the 3 polyominoes are (i) the 2x2 block, (ii) the straight 1x4 block and (iii) the T.

Links

Crossrefs

Cf. A056877, A142886, A006746.

Formula

a(n) = A056877(n) + A142886(n) + A006746(n).

Extensions

More terms from John Mason, Dec 16 2021

A057420 Axially symmetric n-celled polyominoes with 1 hole.

Original entry on oeis.org

1, 3, 8, 25, 45, 137, 221, 650, 1006, 2857, 4370, 12050, 18417, 49516, 76037, 200184, 309411, 800440, 1245934, 3176482
Offset: 9

Views

Author

N. J. A. Sloane, Sep 05 2000

Keywords

Links

Crossrefs

Cf. A006746, A057418.
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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