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.

A197459 Number of free poly-[3.6.3.6]-tiles (holes allowed) with n cells (division into rhombi is significant).

Original entry on oeis.org

1, 1, 3, 4, 12, 27, 78, 208, 635, 1859, 5726, 17526, 54620, 170479, 536714, 1694567, 5376764, 17110286, 54631302, 174879997, 561229678, 1805022806, 5817191196, 18781911278, 60744460580
Offset: 1

Views

Author

Joseph Myers, Oct 15 2011

Keywords

Comments

[3.6.3.6] refers to the face configuration of the rhombille tiling. - Peter Kagey, Mar 01 2020
If we draw the short diagonals of each tile in the rhombille tiling, we get a subset of edges of the regular hexagonal grid; two edges are adjacent if and only if the corresponding rhombi are adjacent. These are polyedges where angles are constrained to 120 degrees. So there is a 1-to-1 correspondence with the subset of polyedges counted in A159867 after removing polyedges with angles of 60 and/or 180 degrees. - Joseph Myers, Jul 12 2020
These are also known as polytwigs, by association with their representation as polyedges. - Aaron N. Siegel, May 15 2022

References

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

Links

Crossrefs

Cf. A019988, A159867, A197460, A197461.
Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).

Extensions

a(18)-a(22) from Aaron N. Siegel, May 15 2022
a(23)-a(25) from Bert Dobbelaere, Jun 04 2025

A151541 Number of 2-sided triangular strip polyedges with n cells.

Original entry on oeis.org

1, 3, 8, 32, 123, 523, 2201, 9443, 40341, 172649, 736926, 3141607, 13367012, 56790498, 240919918, 1020753475, 4319803799, 18262494912, 77134873774, 325518862387, 1372679840360, 5784417772262
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Comments

Also number of unrooted self-avoiding walks of n steps on hexagonal [ =triangular ] lattice. - Hugo Pfoertner, Jun 23 2018

Links

Crossrefs

Cf. A037245, A151539, A151540, A159867, A266925.
Asymptotically approaches (1/24)*A001334(n) for increasing n.

Extensions

a(9)-a(13) from Joseph Myers, Oct 05 2011
a(14)-a(22) from Bert Dobbelaere, Mar 23 2025

A151540 Number of 1-sided triangular strip polyedges with n cells.

Original entry on oeis.org

1, 3, 14, 54, 239, 1007, 4375, 18728, 80572, 344651, 1473402, 6280556, 26732173, 113570050, 481832209, 2041461824, 8639576140, 36524803606, 154269617690, 651036955831, 2745359144355
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Links

Crossrefs

Cf. A151539, A151541, A159867.

Extensions

a(9)-a(13) from Joseph Myers, Oct 05 2011
a(14)-a(21) from Bert Dobbelaere, Mar 23 2025

A151539 Number of 1-sided triangular polyedges with n cells.

Original entry on oeis.org

1, 3, 19, 104, 719, 5123, 37936, 286606, 2202201, 17119423, 134401246, 1063570767, 8473332319
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Links

Crossrefs

Cf. A151540, A151541, A159867.

Extensions

a(9) and a(10) from Joseph Myers, Oct 05 2011
a(11)-a(13) from Aaron N. Siegel, May 23 2022
Showing 1-4 of 4 results.

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