A102320 - OEIS

%I #4 Mar 30 2012 18:36:44

%S 1,1,3,4,9,5,33,72,25,7,436,945,300,49,9,8122,17568,5425,784,81,11,

%T 197920,427770,130700,18081,1620,121,13,6007205,12979080,3947050,

%U 535864,45441,2904,169,15,219413116,473981445,143812400,19348042,1599588,95953

%N 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).

%C Column 0 forms A102321. Column 1 forms A102322. The contribution of each term along the main diagonal to column 0 is given by triangle of coefficients A102323.

%e Rows of T begin:

%e [1],

%e [1,3],

%e [4,9,5],

%e [33,72,25,7],

%e [436,945,300,49,9],

%e [8122,17568,5425,784,81,11],

%e [197920,427770,130700,18081,1620,121,13],

%e [6007205,12979080,3947050,535864,45441,2904,169,15],...

%e Matrix square T^2 equals T excluding the main diagonal:

%e [1],

%e [4,9],

%e [33,72,25],

%e [436,945,300,49],

%e [8122,17568,5425,784,81],...

%o (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])}

%Y Cf. A102086, A102321, A102322, A102323.

%K nonn,tabl

%O 0,3

%A _Paul D. Hanna_, Jan 05 2005