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Table of Sprague-Grundy values for M X N Pop-It! hooks read by antidiagonals.
1

%I #41 Feb 14 2024 13:56:27

%S 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,

%T 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,

%U 11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12

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

%C 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.

%C This table seems to have similarities to A354586.

%H Ryan J. Blau, <a href="/A364480/a364480.png">Colored pattern of hook Sprague-Grundy values</a>.

%H Ryan J. Blau, <a href="/A364480/a364480.py.txt">Python Code</a>.

%e Table begins

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...

%e 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...

%e 3, 4, 1, 6, 7, 8, 9, 10, 11, 12, 13, ...

%e 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...

%e 5, 6, 7, 8, 1, 2, 3, 12, 13, ...

%e 6, 7, 8, 9, 2, 3, 12, 13, ...

%e 7, 8, 9, 10, 3, 12, 1, ...

%e 8, 9, 10, 11, 12, 13, ...

%e 9, 10, 11, 12, 13, ...

%e 10, 11, 12, 13, ...

%e 11, 12, 13, ...

%e 12, 13, ...

%e 13, ...

%e ...

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

%Y Cf. A038712 (main diagonal).

%K nonn,tabl,look

%O 1,2

%A _Ryan J. Blau_, _Michael Carrion_, _Djeneba Diop_, _Sarah Dumnich_, _Matt Prudente_, and _Nathan B. Shank_, Jul 26 2023