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A383663 Number of closed knight's tours in the first 2n cells of a 7 X ceiling(2n/7) board.

%I A383663 #16 Jun 23 2025 14:41:19
%S A383663 2,11,58,0,21,1020,9309,1481,34162,1295034,1067638,2213327,50139185,
%T A383663 682189688,144994543,2607067351,53099426601,34524432316,57716933870,
%U A383663 1388556345255,16330667126220,3697750041989,70341043737487,1662805965511580,1250063279938854,2122662114673944
%N A383663 Number of closed knight's tours in the first 2n cells of a 7 X ceiling(2n/7) board.
%C A383663 If n is not a multiple of 7, the rightmost column has only 2n mod 7 rows (see example).
%D A383663 Donald E. Knuth, Hamiltonian paths and cycles. Prefascicle 8a of The Art of Computer Programming (work in progress, 2025).
%H A383663 Don Knuth, <a href="/A383663/b383663.txt">Table of n, a(n) for n = 11..147</a>
%H A383663 Don Knuth, <a href="https://cs.stanford.edu/~knuth/programs/dynaham.w">CWEB program</a> with input parameter board,42,7,0,0,5,0,0.gb [the graph "board(50, 6, 0, 0, 5, 0, 0)" generated by the Stanford GraphBase].
%F A383663 a(7n) = A193054(n).
%e A383663 For n=11, the first of a(11)=2 solutions is
%e A383663   1  4 21  6
%e A383663  20  7  2
%e A383663   3 22  5
%e A383663   8 19 10
%e A383663  11 16 13
%e A383663  14  9 18
%e A383663  17 12 15
%e A383663 and the other is obtained by reflecting the bottom four rows:
%e A383663   1  4 21  6
%e A383663  20  7  2
%e A383663   3 22  5
%e A383663  10 19  8
%e A383663  13 16 11
%e A383663  18  9 14
%e A383663  15 12 17 .
%Y A383663 Cf. A193054, A383660, A383661, A383662, A383664.
%K A383663 nonn
%O A383663 11,1
%A A383663 _Don Knuth_, May 04 2025