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

1,2

Links

Table of n, a(n) for n=1..19.

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

Cf. A323561, A323562, A355127.

Sequence in context: A349154 A112719 A091019 * A219418 A098400 A208791

Adjacent sequences: A355841 A355842 A355843 * A355845 A355846 A355847

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