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Additional information about A237265

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For editorial reasons, some material concerning sequence A237265 has been moved here.

Recursive and iterative algorithms

Recursive algorithm for generating these matrices:

Let k be the number of elements to permute. Let A(k) be the k X k matrix with the answer.

(Begin)
0)If k=1 then A(k)=[1];
1.0) Else:
1.1) Get A(k-1), and rename it as B;
1.2) Copy the (k-1)^2 elements from B: A(k)[y,x]=B[y,x];
1.3) Assign A(k)[i,k]=k for i in 1..(k-1);
1.4) Assign A(k)[k,j]=j-1 for j in 2..k;
1.5) Assign A(k)[k,1]=k;
2) Return A(k)
(End)

Iterative algorithm for generating these matrices:

Let I(k) be the k X k identity matrix; Let A(k) be a k X k matrix referred to below simply as A;

(Begin)
0.a) Assign: A=I(k);
0.b) set j=2; (where j is a nonnegative integer)
0.c) set u=0; (where u is a nonnegative integer)
1) Assign: A[j,j]+u to A[j,j];
2) Assign: A[j,j] for every element at the right in the same row;
3) Assign: (A[j,j]+1) to every element at the left in the same row;
4) Assign: (A[j,j]+1) to A[1,j];
5) Increment: u++;
6) Increment: j++;
7) Repeat the steps from 1 to 6 while j<=k;
8) Transpose A;
9) Return A;
(End)

Cite this page as

R. J. Cano, Additional information about A237265. — From the On-Line Encyclopedia of Integer Sequences® (OEIS®) wiki. (Available at https://oeis.org/wiki/Additional_information_about_A237265)