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).
1, 1, 2, 15, 16, 3, 1000, 1040, 81, 4, 189035, 196080, 14175, 256, 5, 79278446, 82196224, 5866992, 94464, 625, 6, 63263422646, 65585046960, 4667640795, 73281280, 419375, 1296, 7, 86493299281972, 89664824687968, 6376139907030
Offset: 0
Examples
Rows of T begin: [1], [1,2], [15,16,3], [1000,1040,81,4], [189035,196080,14175,256,5], [79278446,82196224,5866992,94464,625,6], [63263422646,65585046960,4667640795,73281280,419375,1296,7]. Matrix fourth power T^4 equals T excluding the main diagonal: [1], [15,16], [1000,1040,81], [189035,196080,14175,256], [79278446,82196224,5866992,94464,625],...
Programs
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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])}
Formula
T(n, 0) = A082162(n) for n>0, with T(0, 0) = 1.
Comments