cp's OEIS Frontend

A348212 Number of transversals in a cyclic diagonal Latin square of order 2n+1.

%I A348212 #30 Aug 28 2023 08:20:33
%S A348212 1,0,15,133,0,37851,1030367,0,1606008513,87656896891,0,
%T A348212 452794797220965,41609568918940625
%N A348212 Number of transversals in a cyclic diagonal Latin square of order 2n+1.
%C A348212 All cyclic diagonal Latin squares of order n have same number of transversals. A similar statement for diagonal transversals is not true (see A342998 and A342997).
%C A348212 All broken diagonals and antidiagonals of cyclic Latin squares are transversals, so a(n) >= 2*n for all n > 1 for which cyclic diagonal Latin squares exist. - _Eduard I. Vatutin_, Mar 22 2022
%C A348212 All cyclic diagonal Latin squares are diagonal Latin squares, so A287645(2n+1) <= a(n) <= A287644(2n+1) for all orders in which cyclic diagonal Latin squares exist. - _Eduard I. Vatutin_, Mar 23 2022
%H A348212 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1407">About the number of transversals in cyclic Latin and cyclic diagonal Latin squares</a> (in Russian).
%H A348212 <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%F A348212 a(n) = A006717(n) * A011655(n+1).
%e A348212 A cyclic diagonal Latin square of order 5
%e A348212   0 1 2 3 4
%e A348212   2 3 4 0 1
%e A348212   4 0 1 2 3
%e A348212   1 2 3 4 0
%e A348212   3 4 0 1 2
%e A348212 has a(3)=15 transversals:
%e A348212   0 . . . .   0 . . . .   . 1 . . .         . . . . 4
%e A348212   . 3 . . .   . . . . 1   2 . . . .         . 3 . . .
%e A348212   . . 1 . .   . . . 2 .   . . . . 3         . . . 2 .
%e A348212   . . . 4 .   . . 3 . .   . . . 4 .         1 . . . .
%e A348212   . . . . 2   . 4 . . .   . . 0 . .   ...   . . 0 . .
%Y A348212 Cf. A006717, A011655, A287644, A287645, A338562, A342997, A342998.
%K A348212 nonn,more,hard
%O A348212 1,3
%A A348212 _Eduard I. Vatutin_, Oct 07 2021