This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A216344 #5 Feb 22 2013 14:40:40
%S A216344 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 A216344 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 A216344 0,256,256,384
%N 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 .
%F A216344 G.f.: (1-2*x+y*x^2)/(1-2*x-y*x+2*y*x^2-y^2*x^3)
%F A216344 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 A216344 Sum_{k, 0<=k<=n} T(n,k) = A034943(n+1) .
%F A216344 Sum_{k, 0<=k<=n} T(n,k)*2^k*(-1/2)^(n-k) = A052955(n) .
%F A216344 T(n+1,1) = A011782(n), T(n+2,2) = 2^n = A000079(n), T(n+3,3) = A045891(n+1) .
%e A216344 Triangle begins :
%e A216344 1
%e A216344 0, 1
%e A216344 0, 1, 1
%e A216344 0, 2, 2, 1
%e A216344 0, 4, 4, 3, 1
%e A216344 0, 8, 8, 7, 4, 1
%e A216344 0, 16, 16, 16, 11, 5, 1
%e A216344 0, 32, 32, 36, 28, 16, 6, 1
%Y A216344 Cf. A034943
%K A216344 nonn,tabl
%O A216344 0,8
%A A216344 _Philippe Deléham_, Sep 04 2012