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

1,2

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.

Links

Table of n, a(n) for n=1..78.

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

Ryan J. Blau, Python Code.

Example

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, ...
  ...

Crossrefs

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

Cf. A038712 (main diagonal).

Sequence in context: A194303 A124755 A354586 * A033810 A253272 A023965

Adjacent sequences: A364477 A364478 A364479 * A364481 A364482 A364483

Keyword

nonn,tabl,look

Author

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

Status

approved