A110314 Inverse of number triangle related to Fibonacci numbers.

1, -1, 1, -2, -2, 1, 0, -6, -3, 1, 0, 0, -12, -4, 1, 0, 0, 0, -20, -5, 1, 0, 0, 0, 0, -30, -6, 1, 0, 0, 0, 0, 0, -42, -7, 1, 0, 0, 0, 0, 0, 0, -56, -8, 1, 0, 0, 0, 0, 0, 0, 0, -72, -9, 1, 0, 0, 0, 0, 0, 0, 0, 0, -90, -10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -110, -11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, -12, 1

Offset

0,4

Comments

Row sums are 1-n^2 with g.f. (1-3x)/(1-x)^3. Diagonal sums are A110315. Inverse of A039948.

Links

Table of n, a(n) for n=0..90.

Formula

T(n, k)=if(n=k, 1, if(n-k=1, -binomial(n, 1), if(n-k=2, -2*binomial(n, 2), 0)))

Example

Rows begin
1;
-1,1;
-2,-2,1;
0,-6,-3,1;
0,0,-12,-4,1;
0,0,0,-20,-5,1;
0,0,0,0,-30,-6,1;

Crossrefs

Sequence in context: A266291 A064045 A258829 * A370890 A152882 A130167

Adjacent sequences: A110311 A110312 A110313 * A110315 A110316 A110317

Keyword

easy,sign,tabl

Author

Paul Barry, Jul 19 2005

Status

approved