A102320 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^2](n-1,k) when n>k>=0, with T(n,n) = (2*n+1).
1, 1, 3, 4, 9, 5, 33, 72, 25, 7, 436, 945, 300, 49, 9, 8122, 17568, 5425, 784, 81, 11, 197920, 427770, 130700, 18081, 1620, 121, 13, 6007205, 12979080, 3947050, 535864, 45441, 2904, 169, 15, 219413116, 473981445, 143812400, 19348042, 1599588, 95953
Offset: 0
Examples
Rows of T begin: [1], [1,3], [4,9,5], [33,72,25,7], [436,945,300,49,9], [8122,17568,5425,784,81,11], [197920,427770,130700,18081,1620,121,13], [6007205,12979080,3947050,535864,45441,2904,169,15],... Matrix square T^2 equals T excluding the main diagonal: [1], [4,9], [33,72,25], [436,945,300,49], [8122,17568,5425,784,81],...
Programs
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PARI
{T(n,k)=local(A=Mat(1),B); for(m=2,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=2*j-1,if(j==1,B[i,j]=(A^2)[i-1,1], B[i,j]=(A^2)[i-1,j]));));A=B);return(A[n+1,k+1])}
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