

A093057


Triangle T(j,k) read by rows, where T(j,k) = number of matrix elements remaining at fixed position in the insitu 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
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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

Table of n, a(n) for n=1..104.


FORMULA

T(j, k)=gcd(j1, k1)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 nonsingleton cycles, A093056 length of longest cycle, A050873 GCD(u, v).
Sequence in context: A039655 A103775 A331594 * A065334 A356945 A162590
Adjacent sequences: A093054 A093055 A093056 * A093058 A093059 A093060


KEYWORD

nonn,tabl


AUTHOR

Hugo Pfoertner, Mar 22 2004


STATUS

approved



