A204040 Triangle T(n,k), read by rows, given by (0, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 2, 1, 0, 0, 4, 1, 0, -4, 4, 6, 1, 0, -4, -8, 12, 8, 1, 0, 4, -24, -4, 24, 10, 1, 0, 12, -8, -60, 16, 40, 12, 1, 0, 4, 56, -84, -96, 60, 60, 14, 1, 0, -20, 88, 84, -272, -100, 136, 84, 16, 1, 0, -28, -40

Offset: 0

Author

Philippe Deléham, Jan 27 2012

Keywords

• sign
• tabl

Comments

Antidiagonal sums : periodic sequence 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, ... (see A007877 or A098178).Riordan array (1, x*(1+x)/(1-x+2*x^2)) .

Examples

			Triangle begins :
1
0, 1
0, 2, 1
0, 0, 4, 1
0, -4, 4, 6, 1
0, -4, -8, 12, 8, 1
0, 4, -24, -4, 24, 10, 1
0, 12, -8, -60, 16, 40, 12, 1
0, 4, 56, -84, -96, 60, 60, 14, 1
0, -20, 88, 84, -272, -100, 136, 84, 16, 1
		

Crossrefs

Cf. A005408.

Formula

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2, k-1) - 2*T(n-2,k).

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

T(n,n) = n = A000012(n), T(n+1,n) = 2n = A005843(n), T(n+2,n) = A046092(n-1) for n>0, T(n+1,1) = A078050(n)*(-1)^n.

Sum_{k, 0<=k<=n} T(n,k) = A060747(n) = A005408(n-1).