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 A093057 Triangle T(j,k) read by rows, where T(j,k) = number of matrix elements remaining at fixed position in the in-situ transposition of a rectangular j X k matrix (singleton cycles). 2
 0, 0, 1, 0, 0, 2, 0, 1, 0, 3, 0, 0, 0, 0, 4, 0, 1, 2, 1, 0, 5, 0, 0, 0, 0, 0, 0, 6, 0, 1, 0, 3, 0, 1, 0, 7, 0, 0, 2, 0, 0, 2, 0, 0, 8, 0, 1, 0, 1, 4, 1, 0, 1, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 1, 2, 3, 0, 5, 0, 3, 2, 1, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 1, 0, 1, 0, 1, 6, 1, 0, 1, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Elements (1,1) and (j,k) which always remain at their old position are not counted. See A093055 for details of storage, another example, references and links. LINKS FORMULA T(j, k)=gcd(j-1, k-1)-1. EXAMPLE a(8)=T(3,5)=1 because there is one fixed element at position 8 in the transposition from (1 2 3 4 5)(6 7 8 9 10)(11 12 13 14 15) -> (1 6 11)(2 7 12)(3 8 13)(4 9 14)(5 10 15). The fixed first and last elements 1 and 15 are not counted. CROSSREFS Cf. A093055 number of non-singleton cycles, A093056 length of longest cycle, A050873 GCD(u, v). Sequence in context: A039655 A103775 A331594 * A065334 A162590 A276424 Adjacent sequences:  A093054 A093055 A093056 * A093058 A093059 A093060 KEYWORD nonn,tabl AUTHOR Hugo Pfoertner, Mar 22 2004 STATUS approved

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Last modified May 18 21:30 EDT 2021. Contains 344003 sequences. (Running on oeis4.)