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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A197549 Number of free poly-IH10-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 1, 5, 16, 62, 276, 1222, 5563, 25805, 120909, 572011, 2727485, 13089106, 63164265
Offset: 1

Views

Author

Joseph Myers, Oct 16 2011

Keywords

Comments

Equivalently, polyhexes where two polyhexes are considered equivalent if and only if they are related by a translation or a rotation of order 3.

References

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

Crossrefs

Cf. A000228, A001207, A006535, A057973, A197550, A197551, A197552, A197553, A197554.

A197550 Number of free poly-IH8-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 3, 7, 28, 99, 433, 1852, 8463, 38798, 181889, 858570, 4093739, 19636172, 94759074
Offset: 1

Views

Author

Joseph Myers, Oct 16 2011

Keywords

Comments

Equivalently, one-sided polybricks, or polyhexes where two polyhexes are considered equivalent if and only if they are related by a translation or a rotation of order 2.

References

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

Links

  • Tom McLean, IH8.

Crossrefs

Cf. A000228, A001207, A006535, A057973, A197549, A197551, A197552, A197553, A197554.

A197551 Number of free poly-IH18-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 1, 4, 10, 37, 147, 637, 2823, 13020, 60649, 286549, 1364667, 6547108, 31586568
Offset: 1

Views

Author

Joseph Myers, Oct 16 2011

Keywords

Comments

Equivalently, polyhexes where two polyhexes are considered equivalent if and only if they are related by a translation, a rotation of order 3 or a reflection or glide reflection in a line perpendicular to the sides of the hexagons.

References

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

Crossrefs

Cf. A000228, A001207, A006535, A057973, A197549, A197550, A197552, A197553, A197554.

A197552 Number of free poly-IH19-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 1, 4, 10, 36, 146, 631, 2815, 12987, 60601, 286376, 1364399, 6546220, 31585133
Offset: 1

Views

Author

Joseph Myers, Oct 16 2011

Keywords

Comments

Equivalently, polyhexes where two polyhexes are considered equivalent if and only if they are related by a translation, a rotation of order 3 or a reflection or glide reflection in a line parallel to the sides of the hexagons.

References

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

Crossrefs

Cf. A000228, A001207, A006535, A057973, A197549, A197550, A197551, A197553, A197554.

A197553 Number of free poly-IH12-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 2, 7, 24, 99, 416, 1852, 8386, 38797, 181530, 858560, 4092031, 19636098, 94750833
Offset: 1

Views

Author

Joseph Myers, Oct 16 2011

Keywords

Comments

Equivalently, polyhexes where two polyhexes are considered equivalent if and only if they are related by a translation or a reflection or glide reflection in a line in one fixed direction perpendicular to the sides of the hexagons.

References

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

Crossrefs

Cf. A000228, A001207, A006535, A057973, A197549, A197550, A197551, A197552, A197554.

A197554 Number of free poly-IH14-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 2, 7, 24, 98, 415, 1846, 8378, 38764, 181482, 858387, 4091763, 19635210, 94749398
Offset: 1

Views

Author

Joseph Myers, Oct 16 2011

Keywords

Comments

Equivalently, polyhexes where two polyhexes are considered equivalent if and only if they are related by a translation or a reflection or glide reflection in a line in one fixed direction parallel to the sides of the hexagons.

References

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

Crossrefs

Cf. A000228, A001207, A006535, A057973, A197549, A197550, A197551, A197552, A197553.

A344211 Number of generalized polyforms on the rhombitrihexagonal tiling with n cells.

Original entry on oeis.org

1, 3, 2, 7, 16, 60, 201, 838, 3407, 14767, 64200, 284676, 1269981, 5715325, 25854146, 117576949, 536918541, 2461230475, 11319321354, 52212782646
Offset: 0

Views

Author

Peter Kagey, May 11 2021

Keywords

Comments

This sequence counts "free" polyforms where holes are allowed. This means that two polyforms are considered the same if one is a rigid transformation (translation, rotation, reflection or glide reflection) of the other.

Links

Crossrefs

Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).

Extensions

a(11)-a(19) from Bert Dobbelaere, Jun 05 2025

A369363 Least number of inequivalent cells in a (planar) polyhex with n cells.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 4
Offset: 1

Views

Author

Pontus von Brömssen, Jan 22 2024

Keywords

Comments

Equivalently, a(n) is the least number of free rooted (or pointed) polyhexes (A369362) corresponding to a given polyhex with n cells.

Links

Crossrefs

Cf. A000228, A367758, A369362, A369364, A369366.

Extensions

a(13)-a(16) from John Mason, Sep 24 2024

A344213 Number of generalized polyforms on the truncated trihexagonal tiling with n cells.

Original entry on oeis.org

1, 3, 3, 14, 50, 261, 1397, 8364, 50643, 315512, 1984853, 12619579, 80802300, 520724842, 3373646060, 21959949924, 143527242317
Offset: 0

Views

Author

Peter Kagey, May 11 2021

Keywords

Comments

This sequence counts "free" polyforms where holes are allowed. This means that two polyforms are considered the same if one is a rigid transformation (translation, rotation, reflection or glide reflection) of the other.

Links

Crossrefs

Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square), A344211 (rhombitrihexagonal).

Extensions

a(10)-a(16) from Bert Dobbelaere, Jun 07 2025

A383908 Number of generalized polyforms with n cells on the snub trihexagonal tiling.

Original entry on oeis.org

1, 3, 3, 7, 23, 69, 228, 766, 2642, 9309, 33382, 120629, 439752, 1613135, 5953061, 22075011, 82204128, 307213215, 1151820825, 4330858682, 16326297768, 61690058385
Offset: 0

Views

Author

Peter Kagey, May 14 2025

Keywords

Comments

A generalized polyform on the snub trihexagonal tiling with n-cells is a collection of n faces connected edgewise. Two polyforms are considered the same they are related by an isometry (translation and/or rotation) of the snub trihexagonal tiling.

Examples

			For n=1, the a(1) = 3 generalized polyforms are the three types of faces: hexagons, hexagon-adjacent triangles, and hexagon-nonadjacent triangles.
For n=2, the a(2) = 3 generalized polyforms are
(1) a hexagon with a hexagon-adjacent triangle,
(2) a hexagon-adjacent triangle with a hexagon-nonadjacent triangle, and
(3) two hexagon-adjacent triangles.

Links

Crossrefs

Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square), A344211 (rhombitrihexagonal), A344213 (truncated trihexagonal).

Extensions

a(12)-a(21) from Bert Dobbelaere, Jun 05 2025
Previous Showing 41-50 of 75 results. Next

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