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A383664 Number of closed knight's tours in the first 2n cells of an 8 X ceiling(2n/8) board.

%I A383664 #14 May 05 2025 15:18:53
%S A383664 4,12,212,0,50,4525,101730,44202,66034,2408624,69362264,55488142,
%T A383664 101343548,2398536889,43391615822,34524432316,52661182514,
%U A383664 1231713564493,20780788492646,13267364410532,21515340977481,552407941427835,10211663162678661,7112881119092574,11873618786859165
%N A383664 Number of closed knight's tours in the first 2n cells of an 8 X ceiling(2n/8) board.
%C A383664 If n is not a multiple of 4, the rightmost column has only 2n mod 8 rows (see example).
%D A383664 Donald E. Knuth, Hamiltonian paths and cycles, Prefascicle 8a of The Art of Computer Programming (work in progress, 2025).
%H A383664 Don Knuth, <a href="/A383664/b383664.txt">Table of n, a(n) for n = 13..96</a>
%H A383664 Don Knuth, <a href="https://cs.stanford.edu/~knuth/programs/dynaham.w">CWEB program</a> with input parameter board,32,8,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase].
%F A383664 a(4n) = A193055(n).
%e A383664 For n=13 the a(13)=4 solutions are
%e A383664   1  4 25 12
%e A383664  24 11  2  5
%e A383664   3 26 13
%e A383664  10 23  6
%e A383664   7 14  9
%e A383664  22 17 20
%e A383664  19  8 15
%e A383664  16 21 18   ;
%e A383664   1  4 25 12
%e A383664  24 11  2  5
%e A383664   3 26 13
%e A383664  10 23  6
%e A383664   7 14  9
%e A383664  20 15 22
%e A383664  15  8 19
%e A383664  18 21 16   ;
%e A383664   1 14 25 22
%e A383664  24 21  2 15
%e A383664  13 26 23
%e A383664  20  3 16
%e A383664  17 12 19
%e A383664   4  9  6
%e A383664   7 18 11
%e A383664  10  5  8   ;
%e A383664   1 14 25 22
%e A383664  24 21  2 15
%e A383664  13 26 23
%e A383664  20  3 16
%e A383664  17 12 19
%e A383664   6  9  4
%e A383664  11 18  7
%e A383664   8  5 10   .
%Y A383664 Cf. A193055, A383660, A383661, A383662, A383663.
%K A383664 nonn
%O A383664 13,1
%A A383664 _Don Knuth_, May 04 2025