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

Author

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

Keywords

• nonn
• tabl
• look

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

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

Crossrefs

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

Cf. A038712 (main diagonal).