A216344 - OEIS

%I #5 Feb 22 2013 14:40:40

%S 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,

%T 36,28,16,6,1,0,64,64,80,68,45,22,7,1,0,128,128,176,160,118,68,29,8,1,

%U 0,256,256,384

%N 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 .

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

%F 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 .

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

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

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

%e Triangle begins :

%e 1

%e 0, 1

%e 0, 1, 1

%e 0, 2, 2, 1

%e 0, 4, 4, 3, 1

%e 0, 8, 8, 7, 4, 1

%e 0, 16, 16, 16, 11, 5, 1

%e 0, 32, 32, 36, 28, 16, 6, 1

%Y Cf. A034943

%K nonn,tabl

%O 0,8

%A _Philippe Deléham_, Sep 04 2012