A238156 Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 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, 0, 2, 0, 2, 3, 0, 2, 7, 4, 0, 2, 11, 16, 5, 0, 2, 15, 36, 30, 6, 0, 2, 19, 64, 91, 50, 7, 0, 2, 23, 100, 204, 196, 77, 8, 0, 2, 27, 144, 385, 540, 378, 112, 9, 0, 2, 31, 196, 650, 1210, 1254, 672, 156, 10, 0, 2, 35, 256, 1015, 2366, 3289, 2640, 1122, 210, 11

Offset: 0

Author

Philippe Deléham, Feb 18 2014

Keywords

• nonn
• tabl

Comments

Row sums are A001519(n+1) = A122367(n).

Diagonal sums are A052969(n).

Examples

			Triangle begins:
1;
0, 2;
0, 2, 3;
0, 2, 7, 4;
0, 2, 11, 16, 5;
0, 2, 15, 36, 30, 6;
0, 2, 19, 64, 91, 50, 7;
0, 2, 23, 100, 204, 196, 77, 8;
0, 2, 27, 144, 385, 540, 278, 112, 9;
0, 2, 31, 196, 650, 1210, 1254, 672, 156, 10;
0, 2, 35, 256, 1015, 2366, 3289, 2640, 1122, 210, 11;
...
		

Crossrefs

Cf. A016742, A004767, A005581, A005583

Formula

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

Sum_{k=0..n} T(n,k)*2^k = 4^n = A000302(n).

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