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 1-5 of 5 results.

A284869 Number of n-step 2-dimensional closed self-avoiding paths on triangular lattice, reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.

Original entry on oeis.org

0, 0, 1, 1, 1, 4, 5, 16, 37, 120, 344, 1175, 3807, 13224, 45645, 161705, 575325, 2074088, 7521818, 27502445, 101134999, 374128188
Offset: 1

Views

Author

Luca Petrone, Apr 04 2017

Keywords

Comments

Differs from A057729 beginning at n = 11, since that sequence includes triangular polyominoes with holes.
a(n) is the number of simply connected polyiamonds with perimeter n. - Walter Trump, Nov 29 2023

Links

Crossrefs

Approaches (1/12)*A036418 for increasing n.
Cf. A057729, A258206, A266549, A316196.

Extensions

a(15) from Hugo Pfoertner, Jun 27 2018
a(16)-a(22) from Walter Trump, Nov 29 2023

A057729 Number of triangular polyominoes (or polyiamonds) [A000577] with perimeter n.

Original entry on oeis.org

0, 0, 1, 1, 1, 4, 5, 16, 37, 120, 345, 1181, 3844, 13429, 46736, 167172
Offset: 1

Views

Author

N. J. A. Sloane, Oct 29 2000

Keywords

References

  • a(10) found by Brendan Owen.

Links

Crossrefs

Cf. A000577, A284869, A316196.

Extensions

Link updated by William Rex Marshall, Dec 16 2009
a(11)-a(12) from Luca Petrone, Apr 04 2017
a(12)-a(16) corrected and extended by John Mason, Jul 26 2021

A316194 Number of symmetric self-avoiding polygons on square lattice with perimeter 2*n, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 1, 1, 3, 4, 16, 23, 87
Offset: 1

Views

Author

Hugo Pfoertner, Jun 27 2018

Keywords

Comments

The sequence includes polygons of 2-fold, i.e., mirror or rotational, and higher (order >= 4) symmetry.

Links

Crossrefs

Cf. A002931, A266549, A316196, A323188, A323189.

A346126 Numbers m such that no self-avoiding walk of length m + 1 on the hexagonal lattice fits into the smallest circle that can enclose a walk of length m.

Original entry on oeis.org

1, 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 19, 20, 22, 23, 24, 25, 27, 31, 32, 34, 37, 38, 39, 40, 42, 43, 44, 45, 48, 49, 55, 56, 57, 58, 60, 61
Offset: 1

Views

Author

Hugo Pfoertner and Markus Sigg, Jul 31 2021

Keywords

Comments

Open and closed walks are allowed. It is conjectured that all optimal paths are closed except for the trivial path of length 1. See the related conjecture in A122226.

Examples

			See link for illustrations of terms corresponding to diameters D <= 8.

Links

Crossrefs

Cf. A122226, A125852, A127399, A127400, A127401, A151541, A284869, A306176, A316196.
Cf. A346123 (similar to this sequence, but for honeycomb net), A346124 (ditto for square lattice).
Cf. A346125, A346127-A346132 (similar to this sequence, but with other sets of turning angles).

A316193 Number of symmetric self-avoiding polygons on honeycomb net with perimeter 2*n, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 3, 1, 10, 5
Offset: 1

Views

Author

Hugo Pfoertner, Jul 03 2018

Keywords

Comments

The sequence includes polygons of 2-fold, i.e., mirror or rotational, and higher (order >= 3) symmetry.

Links

Crossrefs

Cf. A258206, A316194, A316196.
Showing 1-5 of 5 results.

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

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