A102583 Triangular matrix, read by rows, where row n is formed from the first differences of row (n-1) of its inverse matrix square, with an appended '1' for the main diagonal.

1, 1, 1, -2, 3, 1, 13, -19, 7, 1, -209, 310, -115, 15, 1, 7558, -11328, 4315, -575, 31, 1, -584837, 883178, -342761, 46965, -2607, 63, 1, 94047241, -142845383, 56217824, -7856782, 448173, -11199, 127, 1, -30883147262, 47124630966, -18750717425, 2660027115, -154716638, 3969645, -46655, 255, 1

Offset

0,4

Comments

Row sums are: {1,2,2,2,2,2,...}. Column 0 is A102585. Column 1 is A102586.

Links

Table of n, a(n) for n=0..44.

Formula

T(n, k) = [T^-2](n-1, k) - [T^-2](n-1, k-1) for n>k>0, with T(n, n)=1 for n>=0 and T(n, 0) = [T^-2](n-1, 0) for n>0.

Example

Rows of matrix T begin:
[1],
[1,1],
[ -2,3,1],
[13,-19,7,1],
[ -209,310,-115,15,1],
[7558,-11328,4315,-575,31,1],
[ -584837,883178,-342761,46965,-2607,63,1],
[94047241,-142845383,56217824,-7856782,448173,-11199,127,1],...
and is formed from the first differences of the rows
of the inverse matrix square, T^(-2):
[1],
[ -2,1],
[13,-6,1],
[ -209,101,-14,1],
[7558,-3770,545,-30,1],
[ -584837,298341,-44420,2545,-62,1],...

Prog

(PARI) {T(n, k)=local(A=Mat(1), B); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, j]=(A^-2)[i-1, 1], B[i, j]=(A^-2)[i-1, j]-(A^-2)[i-1, j-1])); )); A=B); return(A[n+1, k+1])}

Crossrefs

Cf. A102585, A102586, A102225.

Sequence in context: A107415 A079174 A204137 * A030780 A193683 A145643

Adjacent sequences: A102580 A102581 A102582 * A102584 A102585 A102586

Keyword

sign,tabl

Author

Paul D. Hanna, Jan 22 2005

Status

approved