A216344 Triangle T(n,k), read by rows, given by (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, -1, 1, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938 .

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 4, 3, 1, 0, 8, 8, 7, 4, 1, 0, 16, 16, 16, 11, 5, 1, 0, 32, 32, 36, 28, 16, 6, 1, 0, 64, 64, 80, 68, 45, 22, 7, 1, 0, 128, 128, 176, 160, 118, 68, 29, 8, 1, 0, 256, 256, 384

Offset: 0

Author

Philippe Deléham, Sep 04 2012

Keywords

• nonn
• tabl

Examples

			Triangle begins :
1
0, 1
0, 1, 1
0, 2, 2, 1
0, 4, 4, 3, 1
0, 8, 8, 7, 4, 1
0, 16, 16, 16, 11, 5, 1
0, 32, 32, 36, 28, 16, 6, 1
		

Crossrefs

Cf. A034943

Formula

G.f.: (1-2*x+y*x^2)/(1-2*x-y*x+2*y*x^2-y^2*x^3)

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k-1) + T(n-3,k-2), T(0,0) = T(1,1) = T(2,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0 and T(n,k) = 0 if k<0 or if k>n .

Sum_{k, 0<=k<=n} T(n,k) = A034943(n+1) .

Sum_{k, 0<=k<=n} T(n,k)*2^k*(-1/2)^(n-k) = A052955(n) .

T(n+1,1) = A011782(n), T(n+2,2) = 2^n = A000079(n), T(n+3,3) = A045891(n+1) .