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

0,3

Comments

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

Links

Table of n, a(n) for n=0..30.

Formula

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

Example

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],...

Prog

(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])}

Crossrefs

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

Sequence in context: A059445 A077518 A196242 * A322149 A163480 A037312

Adjacent sequences: A102098 A102099 A102100 * A102102 A102103 A102104

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 29 2004

Status

approved