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 A307171 Maximum number of partial loops in a diagonal Latin square of order n. 0
 0, 0, 0, 12, 8, 21, 53 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A loop in a Latin square is a sequence of cells v1=L[i1,j1] -> v2=L[i1,j2] -> v1=L[i2,j2] -> ... -> v2=L[im,j1] -> v1=L[i1,j1] of length 2*m that consists of a pair of values {v1, v2}. A partial loop is a loop of length < 2*n. LINKS E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian) EXAMPLE For example, the square   2 4 3 5 0 1   1 0 4 3 2 5   0 2 5 4 1 3   5 3 0 1 4 2   4 5 1 2 3 0   3 1 2 0 5 4 has a loop   2 4 . . . .   . . . . . .   . 2 . 4 . .   . . . . . .   4 . . 2 . .   . . . . . . consisting of the sequence of cells L[1,1]=2 -> L[1,2]=4 -> L[3,2]=2 -> L[3,4]=4 -> L[5,4]=2 -> L[5,1]=4 -> L[1,1]=2 with length 6 < 12. The total number of loops for this square is 21, all of which are partial. CROSSREFS Cf. A307167, A307170. Sequence in context: A094332 A324976 A261402 * A040134 A258641 A206478 Adjacent sequences:  A307168 A307169 A307170 * A307172 A307173 A307174 KEYWORD nonn,more AUTHOR Eduard I. Vatutin, Mar 27 2019 STATUS approved

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Last modified October 18 15:21 EDT 2019. Contains 328162 sequences. (Running on oeis4.)