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.

Showing 1-4 of 4 results.

A197462 Number of free poly-[4.6.12]-tiles (holes allowed) with n cells (division into triangles is significant).

Original entry on oeis.org

1, 3, 3, 9, 14, 38, 74, 185, 414, 1026, 2440, 6077, 14926, 37454, 93749, 237035, 599815, 1526020, 3889117, 9944523, 25475398, 65416733, 168277945, 433705325, 1119610147, 2894928713
Offset: 1

Views

Author

Joseph Myers, Oct 15 2011

Keywords

Comments

[4.6.12] refers to the face configuration of the kisrhombille tiling. - Peter Kagey, May 10 2021

References

  • Branko Gruenbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 2.7, 6.2 and 9.4.

Links

Crossrefs

Cf. A197463, A197464.
Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).

Extensions

a(20)-a(26) from Aaron N. Siegel, Jun 03 2022

A030137 Number of one-sided pentagonal n-ominoes (or pentominoes) on the dodecahedron.

Original entry on oeis.org

1, 1, 2, 5, 9, 20, 13, 12, 5, 3, 1, 1
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A030135 (free).
Cf. A030138 (icosahedron), A383491 (rhombic triacontahedron), A383493 (triakis icosahedron), A383495 (pentakis dodecahedron), A383498 (deltoidal hexecontahedron).
Cf. A197463 (kisrhombille tiling).

A383497 Number of polyforms with n cells on the faces of a disdyakis triacontahedron up to rotation.

Original entry on oeis.org

1, 2, 3, 6, 13, 28, 66, 148, 349, 828, 2004, 4860, 11919, 29280, 72348, 179062, 444357, 1104030, 2747476, 6843910, 17067229, 42593112, 106362575, 265693836, 663811498, 1658352602, 4141998151, 10341234170, 25805349073, 64352577616
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "one-sided" polyforms.
The disdyakis triacontahedron is the polyhedral dual of the truncated icosidodecahedron.

Links

Crossrefs

Cf. A383496 (free).
Cf. A030137 (dodecahedron), A030138 (icosahedron), A383491 (rhombic triacontahedron), A383493 (triakis icosahedron), A383495 (pentakis dodecahedron), A383498 (deltoidal hexecontahedron).
Cf. A197463 (kisrhombille tiling).

Extensions

a(1) corrected and a(13)-a(29) from Bert Dobbelaere, Jun 13 2025

A197464 Number of fixed poly-[4.6.12]-tiles (holes allowed) with n cells (division into triangles is significant).

Original entry on oeis.org

12, 18, 36, 75, 168, 386, 888, 2079, 4960, 11988, 29280, 72145, 179112, 447636, 1124956, 2840097, 7197780, 18301738, 46669404, 119308938, 305704584, 784938678, 2019335340, 5204309886, 13435321764, 34738762062, 89952855848
Offset: 1

Views

Author

Joseph Myers, Oct 15 2011

Keywords

References

  • Branko Gruenbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 2.7, 6.2 and 9.4.

Crossrefs

Cf. A197462, A197463.

Extensions

a(20)-a(26) from Aaron N. Siegel, Jun 03 2022
a(27) from Johann Peters, Dec 16 2024
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.