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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

%I

%S 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,

%T 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,

%U 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

%N 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).

%C 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.

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

%e a(8)=T(3,5)=1 because there is one fixed element at position 8 in the transposition from

%e (1 2 3 4 5)(6 7 8 9 10)(11 12 13 14 15) ->

%e (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.

%Y Cf. A093055 number of non-singleton cycles, A093056 length of longest cycle, A050873 GCD(u, v).

%K nonn,tabl

%O 1,6

%A _Hugo Pfoertner_, Mar 22 2004

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Last modified December 6 09:20 EST 2022. Contains 358607 sequences. (Running on oeis4.)