%I #5 Sep 08 2013 13:30:56
%S 1,1,-1,2,0,-1,3,1,-1,-1,5,4,-1,-2,-1,8,10,2,-4,-3,-1,13,22,11,-4,-8,
%T -4,-1,21,45,35,3,-15,-13,-5,-1,34,88,91,34,-20,-32,-19,-6,-1,55,167,
%U 214,128,-1,-65,-56,-26,-7,-1
%N Triangle T(n,k), 0<=k<=n, defined by : T(n,k)=0 if k<0, T(n,k)=0 if k>n,T(0,0)=1, T(1,0)=1, T(1,1)=-1, T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-2,k).
%F Sum{k,0<=k<=n}T(n,k)=A000129(n-1)for n>0 .T(n,0) = Fibonacci(n+1)=A000045(n+1).
%e Triangle begins:
%e 1;
%e 1, -1;
%e 2, 0, -1;
%e 3, 1, -1, -1;
%e 5, 4, -1, -2, -1;
%e 8, 10, 2, -4, -3, -1;
%e 13, 22, 11, -4, -8, -4, -1;
%K sign,tabl
%O 0,4
%A _Philippe Deléham_, Oct 23 2006