A109266 -id:A109266 - cp's OEIS frontend

A109264 Riordan array (1-x-x^2,x(1-x)).

1, -1, 1, -1, -2, 1, 0, 0, -3, 1, 0, 1, 2, -4, 1, 0, 0, 1, 5, -5, 1, 0, 0, -1, -1, 9, -6, 1, 0, 0, 0, -2, -6, 14, -7, 1, 0, 0, 0, 1, -1, -15, 20, -8, 1, 0, 0, 0, 0, 3, 5, -29, 27, -9, 1, 0, 0, 0, 0, -1, 4, 20, -49, 35, -10, 1, 0, 0, 0, 0, 0, -4, -1, 49, -76, 44, -11, 1, 0, 0, 0, 0, 0, 1, -8, -21, 98, -111, 54, -12, 1

Offset: 0

Paul Barry, Jun 24 2005

Rows sums are A109265. Diagonal sums are A109266. Inverse is A109267.

			Rows begin
1;
-1,1;
-1,-2,1;
0,0,-3,1;
0,1,2,-4,1;
0,0,1,5,-5,1;
0,0,-1,-1,9,-6,1;

A238160 A skewed version of triangular array A029653.

Original entry on oeis.org

1, 0, 2, 0, 1, 2, 0, 0, 3, 2, 0, 0, 1, 5, 2, 0, 0, 0, 4, 7, 2, 0, 0, 0, 1, 9, 9, 2, 0, 0, 0, 0, 5, 16, 11, 2, 0, 0, 0, 0, 1, 14, 25, 13, 2, 0, 0, 0, 0, 0, 6, 30, 36, 15, 2, 0, 0, 0, 0, 0, 1, 20, 55, 49, 17, 2, 0, 0, 0, 0, 0, 0, 7, 50, 91, 64, 19, 2, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Feb 18 2014

Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
Row sums are Fib(n+2).
Column sums are A003945(k).
Diagonal sums are (-1)^(n+1)*A109266(n+1).
T(3*n,2*n) = A029651(n).

			Triangle begins:
1;
0, 2;
0, 1, 2;
0, 0, 3, 2;
0, 0, 1, 5, 2;
0, 0, 0, 4, 7, 2;
0, 0, 0, 1, 9, 9, 2;
0, 0, 0, 0, 5, 16, 11, 2;
0, 0, 0, 0, 1, 14, 25, 13, 2;
0, 0, 0, 0, 0, 6, 30, 36, 15, 2;
0, 0, 0, 0, 0, 1, 20, 55, 49, 17, 2;
0, 0, 0, 0, 0, 0, 7, 50, 91, 64, 19, 2;
...

Cf. A029635, A029653, A178524.

G.f.: (1+x*y)/(1-x*y-x^2*y).
T(n,k) = T(n-1,k-1) + T(n-2,k-1), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(n,k) = 0 if k<0 or if k>n.
Sum_{k=0..n} T(n,k)*x^k = A000007(n), A000045(n+2), A026150(n+1), A108306(n), A164545(n), A188168(n+1) for x = 0, 1, 2, 3, 4, 5 respectively.

cp's OEIS Frontend

A109264 Riordan array (1-x-x^2,x(1-x)).

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