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A102098 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^3](n-1,k) when n>k>=0, with T(n,n) = (n+1). 13

%I #5 Mar 30 2012 18:36:44

%S 1,1,2,7,8,3,139,152,27,4,5711,6200,999,64,5,408354,442552,69687,3904,

%T 125,6,45605881,49399320,7724835,416704,11375,216,7,7390305396,

%U 8003532512,1248465852,66464960,1725875,27432,343,8,1647470410551

%N Triangular matrix, read by rows, that satisfies: T(n,k) = [T^3](n-1,k) when n>k>=0, with T(n,n) = (n+1).

%C Column 0 forms A082162. Column 1 forms A102099. Row sums form A102100. This triangle is a variant of A102086.

%F T(n, 0) = A082162(n) for n>0, with T(0, 0) = 1.

%e Rows of T begin:

%e [1],

%e [1,2],

%e [7,8,3],

%e [139,152,27,4],

%e [5711,6200,999,64,5],

%e [408354,442552,69687,3904,125,6],

%e [45605881,49399320,7724835,416704,11375,216,7],

%e [7390305396,8003532512,1248465852,66464960,1725875,27432,343,8],...

%e Matrix cube T^3 equals T excluding the main diagonal:

%e [1],

%e [7,8],

%e [139,152,27],

%e [5711,6200,999,64],

%e [408354,442552,69687,3904,125],...

%o (PARI) {T(n,k)=local(A=matrix(1,1),B);A[1,1]=1; for(m=2,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=j,if(j==1,B[i,j]=(A^3)[i-1,1], B[i,j]=(A^3)[i-1,j]));));A=B);return(A[n+1,k+1])}

%Y Cf. A082162, A102099, A102100, A102086.

%K nonn,tabl

%O 0,3

%A _Paul D. Hanna_, Dec 29 2004

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