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%I #5 Sep 08 2013 13:30:56
%S 1,1,2,2,3,2,3,7,5,2,5,13,14,7,2,8,25,32,23,9,2,13,46,71,62,34,11,2,
%T 34,151,304,367,295,163,62,15,2,55,269,604,827,767,505,238,79,17,2
%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)=2, 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)=A078057(n) .T(n,0) = Fibonacci(n+1)=A000045(n+1).
%e Triangle begins:
%e 1;
%e 1, 2;
%e 2, 3, 2;
%e 3, 7, 5, 2;
%e 5, 13, 14, 7, 2;
%e 8, 25, 32, 23, 9, 2;
%e 13, 46, 71, 62, 34, 11, 2;
%e 21, 84, 149, 156, 105, 47, 13, 2;
%e 34, 151, 304, 367, 295, 163, 62, 15, 2;
%K nonn,tabl
%O 0,3
%A _Philippe Deléham_, Oct 23 2006
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