cp's OEIS Frontend

A355844 a(n) is the number of different self-avoiding (n-1)-move routes for a king on an empty n X n chessboard.

%I A355844 #17 Sep 28 2022 01:24:08
%S A355844 1,12,160,1764,17280,156484,1335984,10899404,85743256,654854660,
%T A355844 4880419048,35632524244,255652444992,1806891645852,12605286082848,
%U A355844 86939096972284,593610191062680,4016965725987052,26965990393104248
%N A355844 a(n) is the number of different self-avoiding (n-1)-move routes for a king on an empty n X n chessboard.
%e A355844 n = 3
%e A355844 The squares are numbered as follows:
%e A355844   0 1 2
%e A355844   3 4 5
%e A355844   6 7 8
%e A355844 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.
%e A355844 .
%e A355844 15 routes starting at square 0:
%e A355844   012 015 014 013
%e A355844   041 042 043 045 046 047 048
%e A355844   031 034 036 037
%e A355844 .
%e A355844 19 routes starting at square 1:
%e A355844   103 104
%e A355844   124 125
%e A355844   130 134 136 137
%e A355844   140 142 143 145 146 147 148
%e A355844   152 154 157 158
%e A355844 .
%e A355844 24 routes starting at square 4:
%e A355844   401 403
%e A355844   410 412 413 415
%e A355844   421 425
%e A355844   430 431 436 437
%e A355844   451 452 457 458
%e A355844   463 467
%e A355844   473 475 476 478
%e A355844   485 487
%e A355844 .
%e A355844 Total number of routes: 4*15 + 4*19 + 1*24 = 60 + 76 + 24 = 160.
%Y A355844 Cf. A323561, A323562, A355127.
%K A355844 nonn,walk,more
%O A355844 1,2
%A A355844 _Frank Hollstein_, Jul 18 2022
%E A355844 a(12)-a(15) from _Martin Ehrenstein_, Sep 22 2022
%E A355844 a(16)-a(19) from _Martin Ehrenstein_, Sep 27 2022