A167666 Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

1, 1, 1, 2, 3, 1, 0, 4, 5, 1, 0, 0, 6, 7, 1, 0, 0, 0, 8, 9, 1, 0, 0, 0, 0, 10, 11, 1, 0, 0, 0, 0, 0, 12, 13, 1, 0, 0, 0, 0, 0, 0, 14, 15, 1, 0, 0, 0, 0, 0, 0, 0, 16, 17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 18, 19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 21, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 23, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Nov 08 2009

Keywords

• nonn
• tabl

Comments

Row sums = A111284(n+1), Diagonal sums = A109613(n).

Examples

			Triangle begins :
1 ;
1, 1 ;
2, 3, 1 ;
0, 4, 5, 1 ;
0, 0, 6, 7, 1 ;
0, 0, 0, 8, 9, 1 ;
0, 0, 0, 0, 10, 11, 1 ; ...
		

Crossrefs

Cf. A000012, A005408, A005843

Formula

T(n,k) = 2*T(n-1,k-1) - T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(3,0) = 0, T(3,1) = 4. - Philippe Deléham, Feb 18 2012

G.f.: (1+(1-y)*x+(2+y)*x^2)/(1-y*x)^2. - Philippe Deléham, Feb 18 2012

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A130779(n), A111284(n+1), A167667(n), A167682(n) for x = -1, 0, 1, 2, 3 respectively. - Philippe Deléham, Feb 18 2012