A355844 a(n) is the number of different self-avoiding (n-1)-move routes for a king on an empty n X n chessboard.
1, 12, 160, 1764, 17280, 156484, 1335984, 10899404, 85743256, 654854660, 4880419048, 35632524244, 255652444992, 1806891645852, 12605286082848, 86939096972284, 593610191062680, 4016965725987052, 26965990393104248
Offset: 1
Examples
n = 3 The squares are numbered as follows: 0 1 2 3 4 5 6 7 8 By symmetry, only the routes starting from a corner square (e.g., square 0), one of the 4 side squares (e.g., square 1), and the 1 center square (square 4) need to be considered. . 15 routes starting at square 0: 012 015 014 013 041 042 043 045 046 047 048 031 034 036 037 . 19 routes starting at square 1: 103 104 124 125 130 134 136 137 140 142 143 145 146 147 148 152 154 157 158 . 24 routes starting at square 4: 401 403 410 412 413 415 421 425 430 431 436 437 451 452 457 458 463 467 473 475 476 478 485 487 . Total number of routes: 4*15 + 4*19 + 1*24 = 60 + 76 + 24 = 160.
Extensions
a(12)-a(15) from Martin Ehrenstein, Sep 22 2022
a(16)-a(19) from Martin Ehrenstein, Sep 27 2022