A354586 -id:A354586 - cp's OEIS frontend

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

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

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

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.

			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, ...
  ...

Ryan J. Blau, Colored pattern of hook Sprague-Grundy values.
Ryan J. Blau, Python Code.

Sprague-Grundy values for Toppling Dominoes L's: A354586.

Cf. A038712 (main diagonal).

A354587 Diagonal of Sprague-Grundy values for n X m 2D Toppling Dominoes L's.

Original entry on oeis.org

1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 31, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 49, 1, 3, 1, 63, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 31, 1, 3, 1, 8, 1, 9, 1, 11, 1, 5, 1, 5, 1, 111, 1, 127, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 21, 1, 3, 1, 31, 1, 3

Offset: 1

Ian C Haile, Aug 18 2022

2D Toppling Dominoes is played in the same manner as conventional Toppling Dominoes, with the addition of toppling in the north and south directions. An n X m L is defined as a column of n dominoes and a row of m dominoes intersecting at an endpoint for both row and column. An n X m L comprises n+m-1 dominoes.

It is known that alternate terms are 1.

Ian C Haile, Python program

Main diagonal of A354586 viewed as square array.

cp's OEIS Frontend

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

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