A210239 Triangle, read by rows, given by (2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 2, 2, 2, 5, 3, 2, 9, 12, 5, 2, 13, 28, 25, 8, 2, 17, 52, 74, 50, 13, 2, 21, 84, 167, 177, 96, 21, 2, 25, 124, 320, 470, 397, 180, 34, 2, 29, 172, 549, 1041, 1211, 850, 331, 55, 2, 33, 228, 870, 2034, 3042, 2928, 1758, 600, 89

Offset: 0

Author

Philippe Deléham, Mar 19 2012

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins :
1
2, 2
2, 5, 3
2, 9, 12, 5
2, 13, 28, 25, 8
2, 17, 52, 74, 50, 13
2, 21, 84, 167, 177, 96, 21
2, 25, 124, 320, 470, 397, 180, 34
		

Crossrefs

Cf. A000045, A026150, A112087 (3rd column, n>2).

Formula

G.f.: (1+x+y*x)/(1-x-y*x-y*x^2-y^2*x^2).

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) + T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 2 and T(n,k) = 0 if k<0 or if k>n.

Sum_{k, 0<=k<=n} T(n,k)*x^k = A122803(n), A000007(n), A040000(n), A026150(n+1) for x = -2, -1, 0, 1 respectively.

T(n,n) = Fibonacci(n+2) = A000045(n+2), T(n+1,n) = A067331(n).