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A093057
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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).
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2
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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; internal format)
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OFFSET
| 1,6
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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.
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FORMULA
| T(j, k)=gcd(j-1, k-1)-1.
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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.
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CROSSREFS
| Cf. A093055 number of non-singleton cycles, A093056 length of longest cycle, A050873 GCD(u, v).
Sequence in context: A132178 A039655 A103775 * A065334 A162590 A191258
Adjacent sequences: A093054 A093055 A093056 * A093058 A093059 A093060
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KEYWORD
| nonn,tabl
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 22 2004
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