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%I #15 Nov 24 2023 17:54:22
%S 1,0,5,27,0,4523,127339,0,204330233,11232045257,0
%N Minimum number of diagonal transversals in a semicyclic diagonal Latin square of order 2n+1.
%C 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 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 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 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 Eduard I. Vatutin, <a href="/A366332/a366332.txt">Proving list (best known examples)</a>.
%H <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e Example of horizontally semicyclic diagonal Latin square of order 13:
%e 0 1 2 3 4 5 6 7 8 9 10 11 12
%e 2 3 4 5 6 7 8 9 10 11 12 0 1 (d=2)
%e 4 5 6 7 8 9 10 11 12 0 1 2 3 (d=4)
%e 9 10 11 12 0 1 2 3 4 5 6 7 8 (d=9)
%e 7 8 9 10 11 12 0 1 2 3 4 5 6 (d=7)
%e 12 0 1 2 3 4 5 6 7 8 9 10 11 (d=12)
%e 3 4 5 6 7 8 9 10 11 12 0 1 2 (d=3)
%e 11 12 0 1 2 3 4 5 6 7 8 9 10 (d=11)
%e 6 7 8 9 10 11 12 0 1 2 3 4 5 (d=6)
%e 1 2 3 4 5 6 7 8 9 10 11 12 0 (d=1)
%e 5 6 7 8 9 10 11 12 0 1 2 3 4 (d=5)
%e 10 11 12 0 1 2 3 4 5 6 7 8 9 (d=10)
%e 8 9 10 11 12 0 1 2 3 4 5 6 7 (d=8)
%Y Cf. A071607, A342990, A342997, A342998, A348212, A366331.
%K nonn,more,hard
%O 0,3
%A _Eduard I. Vatutin_, Oct 07 2023
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