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

Author

Paul D. Hanna, Dec 29 2004

Keywords

• nonn
• tabl

Comments

Column 0 forms A102102. Column 1 forms A102103. Row sums form A102104. This triangle is a variant of A102086 and A102098.

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],...
		

Crossrefs

Cf. A102102, A102103, A102104, A102086, A102098.

Programs

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.