Chomp 3 solved

[Ed Pegg]

Erez Sheiner has proved all 3xn chomp positions have a unique winning move,
settling Gale's 52-year uniqueness conjecture.  
https://arxiv.org/abs/2605.23837  

winning move column sequence
(* 1,2,2,3,4,4,5,5,7,6,7,9,8,11,9,10,13,11,14,12,... *)

winning move row sequence
(* 2,3,2,2,3,2,3,2,3,2,2,3,2,3,2,2,3,2,3,2,... *)

cells remaining sequence
(* 1,5,5,8,13,12,18,16,24,20,23,32,27,38,31,34,46,38,51,42,... *)

A029900: board widths whose winning move is row 2.
A029901: board widths whose winning move is row 3.
A029902: for the A029901 widths, the winning column minus one.  

{1,2,2,3,4,4,5,5,7,6,7,9,8,11,9,10,13,11,14,12,13,16,17,14,15,19,16,17,21,18,22,19,24,20,21,26,22,28,23,24,30,25,31,26,27,33,34,28,29,36,30,38,31,32,40,33,34,42,35,36,44,45,37,38,47,39,48,40,50,41,51,42,43,44,53,45,55,46,56,47,58,48,49,60,50,62,51,53,52,64,65,54,55,67,56,57,69,58,71,59,72,60,74,61,62,76,63,77,64,79,65,66,67,81,82,68,69,70,84,86,71,72,88,73,74,90,91,75,76,77,93,94,78,79,96,80,97,81,82,99,83,101,84,85,103,86,104,87,106,88,89,108,90,110,91,92,112,93,94,114,95,115,96,117,97,118,98,119,99,100,101,122,102,123,124,103,104,126,105,128,106,108,107,130,109,132,110,134,111,135,112,113,114,137,139,115,116,141,142,117,118,119,144,120,145,121,122,147,123,149,124,125,151,126,127,153,154,128,129,156,130,157,131,159,132,133,134,161,162,135,164,136,137,166,138,168,139,140,170,141,171,142,143,173,145,144,175,146,177,147,178,148,180,149,181,150,151,183,152,184,153,154,186,155,188,156,157,190,158,192,159,193,160,161,162,195,163,197,164,198,165,200,166,202,167,168,204,169,170,206,171,207,172,208,173,210,174,175,176,212} 

{2,3,2,2,3,2,3,2,3,2,2,3,2,3,2,2,3,2,3,2,2,3,3,2,2,3,2,2,3,2,3,2,3,2,2,3,2,3,2,2,3,2,3,2,2,3,3,2,2,3,2,3,2,2,3,2,2,3,2,2,3,3,2,2,3,2,3,2,3,2,3,2,2,2,3,2,3,2,3,2,3,2,2,3,2,3,2,2,2,3,3,2,2,3,2,2,3,2,3,2,3,2,3,2,2,3,2,3,2,3,2,2,2,3,3,2,2,2,3,3,2,2,3,2,2,3,3,2,2,2,3,3,2,2,3,2,3,2,2,3,2,3,2,2,3,2,3,2,3,2,2,3,2,3,2,2,3,2,2,3,2,3,2,3,2,3,2,3,2,2,2,3,2,3,3,2,2,3,2,3,2,2,2,3,2,3,2,3,2,3,2,2,2,3,3,2,2,3,3,2,2,2,3,2,3,2,2,3,2,3,2,2,3,2,2,3,3,2,2,3,2,3,2,3,2,2,2,3,3,2,3,2,2,3,2,3,2,2,3,2,3,2,2,3,2,2,3,2,3,2,3,2,3,2,3,2,2,3,2,3,2,2,3,2,3,2,2,3,2,3,2,3,2,2,2,3,2,3,2,3,2,3,2,3,2,2,3,2,2,3,2,3,2,3,2,3,2,2,2,3}