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.

Previous Showing 11-14 of 14 results.

A140859 Border-domination number of queen graph for n X n board.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 5, 6, 6, 6, 9, 10, 9, 12, 13, 10, 14, 16, 13, 18, 19, 14, 21, 22, 17, 24, 25, 18, 25, 28, 21, 30
Offset: 1

Views

Author

N. J. A. Sloane, Sep 04 2008

Keywords

References

  • Teresa W. Haynes, Stephen T. Hedetniemi and Michael A. Henning (eds.), Structures of Domination in Graphs, Springer, 2021. See Table 13 on p. 368.

Links

Crossrefs

Cf. A075458.

Formula

2*n - 9/2 - sqrt(8*n^2 - 40*n + 49)/2 <= a(n) <= n-2 for all n > 3, from Sinko and Slater paper. - Andy Huchala, Mar 09 2024

Extensions

a(14)-a(24) from "Structures of Domination in Graphs" added by Andrey Zabolotskiy, Sep 02 2021
a(25)-a(31) from Andy Huchala, Mar 05 2024
a(32) from Andy Huchala, Mar 20 2024

A229803 Domination number for rook graph HR(n) on a triangular board of hexagonal cells. The rook can move along any row of adjacent cells, in any of the three directions.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11
Offset: 1

Views

Author

Stan Wagon, Sep 29 2013

Keywords

Comments

The value for HR(20) was obtained by Rob Pratt, Sep 29 2013, using integer-linear programming.

Examples

			For HR(7), the graph can be dominated by the three vertices 6, 11, 26, where we count down from the top.
This graph was called the Queen graph in the DeMaio and Tran paper, but the moves are those of a rook in the classic hexagonal chess game.

References

  • J. Konhauser, D. Velleman, S. Wagon, Which Way Did the Bicycle Go? Washington, DC, Math. Assoc. of America, 1996, pp. 169-172

Links

Crossrefs

Cf. A075458, A075324, A075561, A006075.

Extensions

a(21)-a(24) from Bird added by Andrey Zabolotskiy, Sep 03 2021

A287392 Domination number for lion's graph on an n X n board.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 81, 81, 81, 81, 81, 100, 100, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 144, 169, 169, 169
Offset: 0

Views

Author

David Nacin, May 24 2017

Keywords

Comments

Minimum number of lions (from Chu shogi, Dai shogi and other Shogi variants) required to dominate an n X n board.

Examples

			For n=6 we need a(6)=4 lions to dominate a 6 X 6 board.

Links

Crossrefs

Cf. A075458.

Programs

  • Mathematica
    Table[Floor[(i+4)/5]^2, {i, 0, 64}]
  • Python
    [int((n+4)/5)**2 for n in range(64)]

Formula

a(n) = floor((n+4)/5)^2.
Sum_{n>=1} 1/a(n) = 5*Pi^2/6. - Amiram Eldar, Aug 15 2022

A362601 Domination number for pawns' graph P(n).

Original entry on oeis.org

1, 2, 5, 8, 12, 16, 23, 28, 33, 44, 49, 56, 70, 78, 85, 104, 111, 120, 141, 152, 161, 188, 197, 208, 237, 250, 261, 296, 307, 320, 357, 372, 385, 428, 441, 456, 501, 518, 533, 584
Offset: 1

Views

Author

Rodolfo Kurchan, Jun 18 2023

Keywords

Comments

Minimum number of white pawns needed to occupy or attack all squares of an n X n chessboard.
Solutions for boards of sizes 1 to 8, 10, 14, 15 from Rodolfo Kurchan.
Solutions for boards of sizes 9, 11, 12, 14 to 18, 20 to 24 from Michael Steinau.
Solution for boards of size 13 and 25 to 40 from M. Achterberg.

Examples

			a(8) = 28 white pawns occupying or attacking all squares of a standard chessboard:
  . . . . . . . .
  . P P P P P P .
  . P . . . . P .
  . P . P P . P .
  . P . . . . P .
  . P . P P . P .
  . P . . . . P .
  P P P P P P P P

Links

Crossrefs

Cf. A075458.
Previous Showing 11-14 of 14 results.

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

Content is available under The OEIS End-User License Agreement.