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.

User: Juris Cernenoks

Juris Cernenoks's wiki page.

Juris Cernenoks has authored 2 sequences.

A238381 Minimal number of V-trominoes needed to prevent any further V-trominoe from being placed on an n X n grid.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 11, 14, 18, 21, 25, 30, 35, 40
Offset: 1

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Author

Juris Cernenoks, Feb 25 2014

Keywords

Comments

The V-trominoes must line up with the squares on the grid (skew placements are not allowed).
a(n) is the independent domination number of a graph with one node per tromino and an edge for each pair of trominoes that conflict. - Rob Pratt, Oct 02 2019

Links

Crossrefs

Cf. A226918.

Extensions

a(13)-a(15) from Rob Pratt, Oct 02 2019

A214294 The maximum number of V-pentominoes covering the cells of square n × n.

Original entry on oeis.org

0, 0, 1, 2, 4, 6, 8, 12, 14, 18, 22, 27, 32, 37, 43, 49, 55, 62, 69, 77
Offset: 1

Views

Author

Juris Čerņenoks, Jul 10 2012

Keywords

Comments

The problem of determining the maximum number of V-pentominoes (or the densest packing) covering the cells of the square n × n was proposed by A. Cibulis.
Problem for the squares 5 × 5, 6 × 6 and 8 × 8 was given in the Latvian Open Mathematics Olympiad 2000 for Forms 6, 8 and 5 respectively.
Solutions for the squares 3 × 3, 5 × 5, 8 × 8, 12 × 12, 16 × 16 are unique under rotation and reflection.

Examples

			There is no way to cover square 3 × 3 with more than just one V-pentomino so a(3)=1.

References

  • A. Cibulis, Equal Pentominoes on the Chessboard, j. "In the World of Mathematics", Kyiv, Vol. 4., No. 3, pp. 80-85, 1998. (In Ukrainian), http://www.probability.univ.kiev.ua/WorldMath/mathw.html
  • A. Cibulis, Pentominoes, Part I, Riga, University of Latvia, 2001, 96 p. (In Latvian)
  • A. Cibulis, From Olympiad Problems to Unsolved Ones, The 12th International Conference "Teaching Mathematics: Retrospective and Perspectives", Šiauliai University, Abstracts, pp. 19-20, 2011.

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