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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A323132 Number of uncrossed unrooted knight's paths of length n on an infinite board.

Original entry on oeis.org

1, 6, 25, 160, 966, 6018, 37079, 227357
Offset: 1

Views

Author

Hugo Pfoertner, Jan 05 2019

Keywords

Comments

Paths which are equivalent under rotation, reflection or reversal are counted only once.

Examples

			See illustrations at Pfoertner link.

Links

Crossrefs

Cf. A003192, A001334, A151541, A272773, A306178, A323131, A323133, A323134.

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

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).

A213451 Number of fixed triangular strip polyedges with n edges.

Original entry on oeis.org

3, 15, 69, 309, 1365, 5973, 25941, 112065, 482067, 2066583, 8834469, 37677603, 160367343
Offset: 1

Views

Author

N. J. A. Sloane, Jun 11 2012

Keywords

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

Crossrefs

Cf. A001334, A151540, A151541.

Formula

Apparently, a(n) = A001334(n)/2 for n >= 1. It needs to be clarified whether the objects described by this sequence are equivalent to the self-avoiding walks on the hexagonal lattice together with a restriction on their orientation. - Hugo Pfoertner, Jul 24 2021

Extensions

Better description and more terms from Joseph Myers, Jun 12 2012
Previous Showing 11-14 of 14 results.

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

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