A102100 -id:A102100 - cp's OEIS frontend

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

Paul D. Hanna, Dec 29 2004

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

			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],...

Cf. A082162, A102099, A102100, A102086.

{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])}

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

A102099 Column 1 of triangular matrix A102098, which shifts upward to exclude the main diagonal under matrix cube.

Original entry on oeis.org

0, 2, 8, 152, 6200, 442552, 49399320, 8003532512, 1784040237288, 525504809786112, 198213959637435608, 93352856625931514024, 53776417402985961020144, 37244016639064540041311632

Offset: 0

Paul D. Hanna, Dec 29 2004

nonn

Column 0 of A102098 is A082162.

Cf. A102098, A082162, A102100.

{a(n)=local(A=matrix(2,2),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+1,2])}

cp's OEIS Frontend

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).

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