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 1-4 of 4 results.

A257952 Number of ways to quarter a 2n X 2n chessboard.

Original entry on oeis.org

1, 1, 5, 37, 766, 43318, 7695805, 4015896016, 6371333036059, 30153126159555641, 431453249608567040694, 18558756256964594960321428, 2411839397220672351872242339314, 945878376319424018440202856702995909, 1121914029089423867715407724741780046405923
Offset: 0

Views

Author

Giovanni Resta, May 14 2015

Keywords

Comments

Number of ways to dissect a 2n X 2n chessboard into 4 congruent pieces. As stated by Thomas R. Parkin in his letter (see Links), the dissections belong to two classes. One in which the cuts divide the chessboard into four pieces which are 90-degree rotationally symmetric, the other in which the square is first bisected in two rectangles and then each rectangle is divided into two pieces which are 180-degree rotationally symmetric.
Two dissections are considered distinct if they belong to two different classes, even if the tile is the same. In both classes reflections and rotations are not counted, and moreover in the second class two dissections are considered the same if they differ only by the orientation of the tiles.

References

  • M. Gardner, The Unexpected Hanging and Other Mathematical Diversions. Simon and Schuster, NY, 1969, p. 189.
  • Popular Computing (Calabasas, CA), Vol. 1 (No. 7, 1973), Problem 15, front cover and page 2.

Links

Crossrefs

Cf. A003213 (another version, but probably incorrect - N. J. A. Sloane, Apr 17 2016), A006067, A064941, A113900, A268606.

Programs

Formula

a(n) = A006067(2n) for n>0. - Jean-François Alcover, Sep 14 2019, after Andrew Howroyd in A006067.

Extensions

a(9)-a(14) from Andrew Howroyd, Apr 18 2016

A271741 Number of ways to dissect a hexagon with side length n exactly into two identical parts in a triangular lattice.

Original entry on oeis.org

1, 8, 731, 982648, 16305532683, 3722056510716702, 11931439930135002524767
Offset: 1

Views

Author

Andrew Howroyd, Apr 15 2016

Keywords

Links

  • G. P. Jelliss, Dissected Hexagons, The Games and Puzzles Journal, Issue 22, January-April 2002.

Crossrefs

Cf. A268606, A271857, A113900.

A271857 Number of ways to dissect a hexagon with side length n exactly into six identical parts in a triangular lattice.

Original entry on oeis.org

1, 2, 12, 173, 5429, 392544, 66961869, 27094069322, 26124568587557, 60352331499840380, 335377713005955826349, 4494480789037552980419332, 145516206571394421594063628243, 11398373584242623552596178870957640, 2162546126021822830176241418936795142991
Offset: 1

Views

Author

Andrew Howroyd, Apr 15 2016

Keywords

Comments

This sequence only enumerates those dissections in which the six pieces are arranged around the center at 60-degree intervals. Other dissections are possible, such as those formed from those trisections which can be further bisected into identical parts.

Links

  • G. P. Jelliss, Dissected Hexagons, The Games and Puzzles Journal, Issue 22, January-April 2002.

Crossrefs

Cf. A113900, A268606, A271741.

A271858 Number of ways to trisect a triangle with side length n exactly into three identical parts in a triangular lattice.

Original entry on oeis.org

0, 1, 1, 2, 5, 20, 56, 276, 2136, 13756, 148352, 2727448, 41044816, 1056334024, 46033137324
Offset: 1

Views

Author

Andrew Howroyd, Apr 15 2016

Keywords

Comments

In the case that n is not divisible by 3 the central triangle is removed, otherwise the dissection would not be possible.

Links

  • G. P. Jelliss, Trisected Triangles, The Games and Puzzles Journal, Issue 22, January-April 2002.

Crossrefs

Cf. A268606, A271857, A113900, A257952.
Showing 1-4 of 4 results.

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

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