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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).
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%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