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A366332 Minimum number of diagonal transversals in a semicyclic diagonal Latin square of order 2n+1.

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%I A366332 #15 Nov 24 2023 17:54:22
%S A366332 1,0,5,27,0,4523,127339,0,204330233,11232045257,0
%N A366332 Minimum number of diagonal transversals in a semicyclic diagonal Latin square of order 2n+1.
%C A366332 A horizontally semicyclic diagonal Latin square is a square where each row r(i) is a cyclic shift of the first row r(0) by some value d(i) (see example). Similarly, a vertically semicyclic diagonal Latin square is a square where each column c(i) is a cyclic shift of the first column c(0) by some value d(i).
%H A366332 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2443">About the spectra of numerical characteristics of different types of cyclic diagonal Latin squsres</a> (in Russian).
%H A366332 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2450">About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 17</a> (in Russian).
%H A366332 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2453">About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 19</a> (in Russian).
%H A366332 Eduard I. Vatutin, <a href="/A366332/a366332.txt">Proving list (best known examples)</a>.
%H A366332 <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A366332 Example of horizontally semicyclic diagonal Latin square of order 13:
%e A366332    0  1  2  3  4  5  6  7  8  9 10 11 12
%e A366332    2  3  4  5  6  7  8  9 10 11 12  0  1  (d=2)
%e A366332    4  5  6  7  8  9 10 11 12  0  1  2  3  (d=4)
%e A366332    9 10 11 12  0  1  2  3  4  5  6  7  8  (d=9)
%e A366332    7  8  9 10 11 12  0  1  2  3  4  5  6  (d=7)
%e A366332   12  0  1  2  3  4  5  6  7  8  9 10 11  (d=12)
%e A366332    3  4  5  6  7  8  9 10 11 12  0  1  2  (d=3)
%e A366332   11 12  0  1  2  3  4  5  6  7  8  9 10  (d=11)
%e A366332    6  7  8  9 10 11 12  0  1  2  3  4  5  (d=6)
%e A366332    1  2  3  4  5  6  7  8  9 10 11 12  0  (d=1)
%e A366332    5  6  7  8  9 10 11 12  0  1  2  3  4  (d=5)
%e A366332   10 11 12  0  1  2  3  4  5  6  7  8  9  (d=10)
%e A366332    8  9 10 11 12  0  1  2  3  4  5  6  7  (d=8)
%Y A366332 Cf. A071607, A342990, A342997, A342998, A348212, A366331.
%K A366332 nonn,more,hard
%O A366332 0,3
%A A366332 _Eduard I. Vatutin_, Oct 07 2023