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A383660 Number of closed knight's tours in the first 2n cells of a 3 X ceiling(2n/3) board.

%I A383660 #15 Jun 23 2025 14:41:01
%S A383660 4,0,4,24,16,56,306,176,456,2632,1536,4828,26788,15424,44952,254288,
%T A383660 147728,448032,2502568,1448416,4310048,24228704,14060048,42195584,
%U A383660 236335248,136947616,409403328,2297294496,1332257856,3989883552,22366625344,12965578752,38798663104,217604833360,126169362176
%N A383660 Number of closed knight's tours in the first 2n cells of a 3 X ceiling(2n/3) board.
%C A383660 If n is not a multiple of 3, the rightmost column has only 2n mod 3 rows (see example).
%D A383660 Donald E. Knuth, Hamiltonian paths and cycles, Prefascicle 8a of The Art of Computer Programming (work in progress, 2025).
%H A383660 Don Knuth, <a href="/A383660/b383660.txt">Table of n, a(n) for n = 11..150</a>
%H A383660 Don Knuth, <a href="https://cs.stanford.edu/~knuth/programs/dynaham.w">CWEB program</a> with input parameter board,100,3,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase.
%F A383660 a(3n) = A070030(n).
%e A383660 For n=11 the a(11)=4 solutions are
%e A383660   1  4  7 10 17 20 15 12
%e A383660   6  9  2 21 14 11 18
%e A383660   3 22  5  8 19 16 13    ;
%e A383660   1  4  7 14 11 20  9 18
%e A383660   6 15  2 21  8 17 12
%e A383660   3 22  5 16 13 10 19    ;
%e A383660   1  4 21 12 15  6 17  8
%e A383660  20 11  2  5 18  9 14
%e A383660   3 22 19 10 13 16  7    ;
%e A383660   1  4 21 18  9  6 11 14
%e A383660  20 17  2  5 12 15  8
%e A383660   3 22 19 16  7 10 13    .
%Y A383660 Cf. A070030, A383661, A383662, A383663, A383664.
%K A383660 nonn
%O A383660 11,1
%A A383660 _Don Knuth_, May 04 2025