A114116 -id:A114116 - cp's OEIS frontend

A114117 Inverse of 1's counting matrix A114116.

1, 0, 1, -2, 1, 1, -1, -1, 1, 1, 0, -2, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, 0, -2, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1

Offset: 0

Paul Barry, Nov 13 2005

Row sums are (1,1,0,0,0,.....) with g.f. 1+x. Diagonal sums have g.f. (1-x^2-x^3)/(1-x^3). Product of A114115 and the first difference matrix (1-x,x).

			Triangle begins
  1;
  0, 1;
 -2, 1, 1;
 -1,-1, 1, 1;
  0,-2, 0, 1, 1;
  0,-1,-1, 0, 1, 1;
  0, 0,-2, 0, 0, 1, 1;
  0, 0,-1,-1, 0, 0, 1, 1;

Cf. A114115, A114116.

T(n, k) = Sum_{j=0..n} Sum_{i=0..n} C(floor((n+i)/2), j)*C(j, floor((n+i)/2))*(2*C(0, j-k)-C(1, j-k)).

A114115 Inverse of number triangle A114114.

Original entry on oeis.org

1, -1, 1, 2, -2, 1, -3, 3, -2, 1, 2, -2, 2, -2, 1, 0, 0, -1, 2, -2, 1, 2, -2, 2, -2, 2, -2, 1, -5, 5, -4, 3, -2, 2, -2, 1, 2, -2, 2, -2, 2, -2, 2, -2, 1, 0, 0, 0, 0, -1, 2, -2, 2, -2, 1, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 1, -2, 2, -3, 4, -4, 3, -2, 2, -2, 2, -2, 1, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 1

Offset: 0

Paul Barry, Nov 13 2005

Row sums are A088705. Product with partial sum matrix (1/(1-x),x) gives A114116.

			Triangle begins
1;
-1, 1;
2,-2, 1;
-3, 3,-2, 1;
2,-2, 2,-2, 1;
0, 0,-1, 2,-2, 1;
2,-2, 2,-2, 2,-2, 1;

cp's OEIS Frontend

A114117 Inverse of 1's counting matrix A114116.

Views

Author

Keywords

Comments

Examples

Crossrefs