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).

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

Offset: 1

Author

Hugo Pfoertner, Mar 22 2004

Keywords

• nonn
• tabl

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.

Examples

			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).

Formula

T(j, k)=gcd(j-1, k-1)-1.