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.

A030444 Number of fixed n-celled polyknights.

Original entry on oeis.org

1, 4, 28, 234, 2162, 20972, 209608, 2135572, 22049959, 229939414, 2416816416, 25569786440, 272057195864
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

A polyknight is a variant of a polyomino in which two tiles a knight's move apart are considered adjacent. A polyknight need not be connected in the sense of a polyomino.

References

  • G. Aleksandrowicz and G. Barequet, Parallel enumeration of lattice animals, Proc. 5th Int. Frontiers of Algorithmics Workshop, Zhejiang, China, Lecture Notes in Computer Science, 6681, Springer-Verlag, 90-99, May 2011.

Crossrefs

Cf. A030445, A030446, A030447, A030448.

Extensions

Corrected and extended by Guenter Stertenbrink (Sterten(AT)aol.com), May 23 2004
12th term from Gill Barequet, May 24 2011
a(13) from John Mason, Jan 13 2023

A030445 Number of one-sided n-celled polyknights.

Original entry on oeis.org

1, 2, 8, 68, 550, 5328, 52484, 534793, 5513338, 57494308, 604212943, 6392547793, 68014392915
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

A polyknight is a variant of a polyomino in which two tiles a knight's move apart are considered adjacent. A polyknight need not be connected in the sense of a polyomino.

Examples

			The 2 polyknights with 2 cells:
  X.. ..X
  ..X X..
The 8 polyknights with 3 cells:
  X. X.. X.. X... X.X .X. .X. X...
  .. ... ..X .... ... X.. ..X ...X
  .X .X. ... .X.. .X. ..X X.. .X..
  .. ... .X. ...X
  X. ..X

Crossrefs

Cf. A030444, A030446, A030447, A030448.

Extensions

Corrected and extended by Joseph Myers, May 21 2004
a(12)-a(13) from John Mason, Jan 13 2023

A030447 Number of n-celled polyknights with bilateral symmetry.

Original entry on oeis.org

1, 0, 4, 2, 30, 32, 274, 403, 2694, 4604, 27365, 50777, 282343
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

A polyknight is a variant of a polyomino in which two tiles a knight's move apart are considered adjacent. A polyknight need not be connected in the sense of a polyomino.

Crossrefs

Cf. A030445, A030444, A030446, A030448.

Extensions

Corrected and extended by Joseph Myers, May 21 2004
a(12)-a(13) from John Mason, Jan 13 2023

A030448 Number of n-celled polyknights without bilateral symmetry.

Original entry on oeis.org

0, 1, 2, 33, 260, 2648, 26105, 267195, 2755322, 28744852, 302092789, 3196248508, 34007055286
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

A polyknight is a variant of a polyomino in which two tiles a knight's move apart are considered adjacent. A polyknight need not be connected in the sense of a polyomino.

Crossrefs

Cf. A030445, A030444, A030446, A030447.

Extensions

Corrected and extended by Joseph Myers, May 21 2004
a(12)-a(13) from John Mason, Jan 13 2023

A363382 Three-dimensional polyknights, identifying rotations and reflections.

Original entry on oeis.org

1, 1, 12, 203, 5552, 182490, 6455845, 237152245
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 30 2023

Keywords

Comments

Polyknights in two dimension (A030446) have 8 neighborhood vectors, [+-1, +-2] and [+-2, +-1]. In three dimensions the 24 neighborhood vectors are [0, +-1, +-2] (four choices of signs) and its six permutations.
Showing 1-5 of 5 results.

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

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