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 1-10 of 11 results. Next

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

A316195 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set +-Pi/5, +-3*Pi/5, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 2, 1, 18, 45, 441
Offset: 1

Views

Author

Hugo Pfoertner, Jun 26 2018

Keywords

Comments

Holes are excluded, i.e., the boundary path may nowhere touch or intersect itself.

Links

Crossrefs

Cf. A306175, A258206, A266549, A284869.

A036418 Number of self-avoiding polygons with perimeter n on hexagonal [ =triangular ] lattice.

Original entry on oeis.org

0, 0, 2, 3, 6, 15, 42, 123, 380, 1212, 3966, 13265, 45144, 155955, 545690, 1930635, 6897210, 24852576, 90237582, 329896569, 1213528736, 4489041219, 16690581534, 62346895571, 233893503330, 880918093866, 3329949535934
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

References

  • B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 459.

Links

Crossrefs

Cf. A001334, A284869.

A316197 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set +-Pi/7, +-3*Pi/7, +-5*Pi/7, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 3, 4, 83, 533, 8329
Offset: 1

Views

Author

Hugo Pfoertner, Jun 28 2018

Keywords

Links

Crossrefs

Cf. A306177, A258206, A266549, A284869, A316195.

A316196 Number of symmetric self-avoiding polygons on hexagonal lattice with perimeter n, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 1, 1, 1, 4, 3, 10, 9, 36, 27, 129, 90, 449, 331
Offset: 1

Views

Author

Hugo Pfoertner, Jun 27 2018

Keywords

Links

Crossrefs

Cf. A036418, A284869, A306176.

A316192 Number of self-avoiding polygons with perimeter n and sides = 1 that have vertex angles from the set 0, +-Pi/6, +-*Pi/3, +-Pi/2, +-2*Pi/3, +-5*Pi/6, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 1, 3, 4, 22, 69, 418, 2210, 14024
Offset: 1

Views

Author

Hugo Pfoertner, Jul 07 2018

Keywords

Comments

Holes are excluded, i.e., the boundary path may nowhere touch or intersect itself.

Links

Crossrefs

Cf. A258206, A266549, A284869, A306182, A316195, A316197, A316198, A316199, A316200, A316201.

A316200 Number of self-avoiding polygons with perimeter n and sides = 1 that have vertex angles from the set 0, +-Pi/5, +-2*Pi/5, +-3*Pi/5, +-4*Pi/5, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 0, 2, 2, 10, 15, 124, 352, 2378, 19405
Offset: 1

Views

Author

Hugo Pfoertner, Jul 07 2018

Keywords

Comments

Holes are excluded, i.e., the boundary path may nowhere touch or intersect itself.

Links

Crossrefs

Cf. A258206, A266549, A284869, A306180, A316192, A316195, A316197, A316198, A316199, A316201.

A316201 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set +-Pi/11, +-3*Pi/11, +-5*Pi/11, +-7*Pi/11, +-9*Pi/11, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 8, 19, 720, 10578
Offset: 1

Views

Author

Hugo Pfoertner, Jul 07 2018

Keywords

Comments

Holes are excluded, i.e., the boundary path may nowhere touch or intersect itself.

Links

Crossrefs

Cf. A258206, A266549, A284869, A306181, A316192, A316195, A316197, A316198, A316199, A316200.

A323134 Number of polygons made of uncrossed knight's paths of length 2*n on an infinite board.

Original entry on oeis.org

0, 3, 13, 178, 3031, 64866
Offset: 1

Views

Author

Hugo Pfoertner, Jan 05 2019

Keywords

Examples

			See Pfoertner link.

Links

Crossrefs

Cf. A003192, A157416, A258206, A266549, A284869, A316198.

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).
Showing 1-10 of 11 results. Next

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

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