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A355844
a(n) is the number of different self-avoiding (n-1)-move routes for a king on an empty n X n chessboard.
0
1, 12, 160, 1764, 17280, 156484, 1335984, 10899404, 85743256, 654854660, 4880419048, 35632524244, 255652444992, 1806891645852, 12605286082848, 86939096972284, 593610191062680, 4016965725987052, 26965990393104248
OFFSET
1,2
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,walk,more
AUTHOR
Frank Hollstein, Jul 18 2022
EXTENSIONS
a(12)-a(15) from Martin Ehrenstein, Sep 22 2022
a(16)-a(19) from Martin Ehrenstein, Sep 27 2022
STATUS
approved