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).

1, 1, 2, 7, 8, 3, 139, 152, 27, 4, 5711, 6200, 999, 64, 5, 408354, 442552, 69687, 3904, 125, 6, 45605881, 49399320, 7724835, 416704, 11375, 216, 7, 7390305396, 8003532512, 1248465852, 66464960, 1725875, 27432, 343, 8, 1647470410551

Offset: 0

Author

Paul D. Hanna, Dec 29 2004

Keywords

• nonn
• tabl

Comments

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

Examples

			Rows of T begin:
[1],
[1,2],
[7,8,3],
[139,152,27,4],
[5711,6200,999,64,5],
[408354,442552,69687,3904,125,6],
[45605881,49399320,7724835,416704,11375,216,7],
[7390305396,8003532512,1248465852,66464960,1725875,27432,343,8],...
Matrix cube T^3 equals T excluding the main diagonal:
[1],
[7,8],
[139,152,27],
[5711,6200,999,64],
[408354,442552,69687,3904,125],...
		

Crossrefs

Cf. A082162, A102099, A102100, A102086.

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^3)[i-1,1], B[i,j]=(A^3)[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.