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A102101 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^4](n-1,k) when n>k>=0, with T(n,n) = (n+1).

%I A102101 #5 Mar 30 2012 18:36:44
%S A102101 1,1,2,15,16,3,1000,1040,81,4,189035,196080,14175,256,5,79278446,
%T A102101 82196224,5866992,94464,625,6,63263422646,65585046960,4667640795,
%U A102101 73281280,419375,1296,7,86493299281972,89664824687968,6376139907030
%N A102101 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^4](n-1,k) when n>k>=0, with T(n,n) = (n+1).
%C A102101 Column 0 forms A102102. Column 1 forms A102103. Row sums form A102104. This triangle is a variant of A102086 and A102098.
%F A102101 T(n, 0) = A082162(n) for n>0, with T(0, 0) = 1.
%e A102101 Rows of T begin:
%e A102101 [1],
%e A102101 [1,2],
%e A102101 [15,16,3],
%e A102101 [1000,1040,81,4],
%e A102101 [189035,196080,14175,256,5],
%e A102101 [79278446,82196224,5866992,94464,625,6],
%e A102101 [63263422646,65585046960,4667640795,73281280,419375,1296,7].
%e A102101 Matrix fourth power T^4 equals T excluding the main diagonal:
%e A102101 [1],
%e A102101 [15,16],
%e A102101 [1000,1040,81],
%e A102101 [189035,196080,14175,256],
%e A102101 [79278446,82196224,5866992,94464,625],...
%o A102101 (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^4)[i-1,1], B[i,j]=(A^4)[i-1,j]));));A=B);return(A[n+1,k+1])}
%Y A102101 Cf. A102102, A102103, A102104, A102086, A102098.
%K A102101 nonn,tabl
%O A102101 0,3
%A A102101 _Paul D. Hanna_, Dec 29 2004