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: Michael Carrion

Michael Carrion's wiki page.

Michael Carrion has authored 2 sequences.

A364480 Table of Sprague-Grundy values for M X N Pop-It! hooks read by antidiagonals.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 1, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 1, 9, 9, 9, 9, 10, 10, 10, 10, 2, 2, 10, 10, 10, 10, 11, 11, 11, 11, 3, 3, 3, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
Offset: 1

Views

Author

Ryan J. Blau, Michael Carrion, Djeneba Diop, Sarah Dumnich, Matt Prudente, and Nathan B. Shank, Jul 26 2023

Keywords

Comments

Pop-It! is played on an M X N lattice graph with a "pip" at each node. A move consists of popping any number of pips that are all collinear on the same horizontal or vertical line. A hook h(a,b) is defined as two lines of lengths a and b connected by a corner pip. The total number of pips of a hook h(a,b) is a+b+1.
This table seems to have similarities to A354586.

Examples

			Table begins
   1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
   2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
   3,  4,  1,  6,  7,  8,  9, 10, 11, 12, 13, ...
   4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
   5,  6,  7,  8,  1,  2,  3, 12, 13, ...
   6,  7,  8,  9,  2,  3, 12, 13, ...
   7,  8,  9, 10,  3, 12,  1, ...
   8,  9, 10, 11, 12, 13, ...
   9, 10, 11, 12, 13, ...
  10, 11, 12, 13, ...
  11, 12, 13, ...
  12, 13, ...
  13, ...
  ...

Links

Crossrefs

Sprague-Grundy values for Toppling Dominoes L's: A354586.
Cf. A038712 (main diagonal).

A364451 a(n) is the number of trees of diameter 4 with n vertices that are N-games in peg duotaire.

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 5, 7, 10, 13, 18, 22, 29, 34, 42, 49, 60, 69, 86, 100, 121, 139, 164, 187, 219, 252, 296, 343, 400, 458, 532, 605, 696, 794, 917, 1050, 1214, 1389, 1599, 1823, 2087, 2371, 2710, 3080, 3521
Offset: 1

Views

Author

Michael Carrion, Nathan Hurtig, Maggie X. Lai, Sarah Lohrey, Brittany Ohlinger, Jul 25 2023

Keywords

Comments

Peg duotaire is an impartial normal-play two-player game played on a simple graph, in which each vertex starts with a peg in it. If all vertices have a peg (i.e. the first turn), a move consists of removing some peg from a vertex.
If some vertex does not have a peg, then a move hops one peg over another, landing in an adjacent hole and removing the jumped peg. Formally, it is three vertices x, y, z where x, y are adjacent and y, z are adjacent, and x, y have pegs and z does not. After the move, x, y do not have pegs and z does.
Note than this sequence is always less than or equal to the number of trees of diameter 4 with n vertices, see A000094.

Examples

			There is only one tree of diameter 4 with 5 vertices. It is an N-game, as evidenced by the below winning strategy for the first player. We use 1 to represent a vertex with a peg and 0 otherwise.
   1-1-1-1-1
       |
   1-0-1-1-1
       |     (move is forced)
   1-1-0-0-1
       |
   0-0-1-0-1 (no moves remain)

References

  • E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays. Vol. 1, CRC Press, 2001.

Links

Crossrefs

Cf. A000094.

Formula

a(n) <= A000094(n).

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

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