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Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=3, T(1,0) = T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
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%I #7 Mar 15 2013 12:40:21

%S 1,1,1,1,2,0,0,3,2,0,0,3,5,0,0,0,0,8,5,0,0,0,0,8,13,0,0,0,0,0,0,21,13,

%T 0,0,0,0,0,0,21,34,0,0,0,0,0,0,0,0,55,34,0,0,0,0,0,0,0,0,55,89,0,0,0,

%U 0,0,0,0

%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=3, T(1,0) = T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

%F T(n,n) = T(n+1,n) = A001519(n+1).

%F T(n,n+1) = T(n,n+2) = A001906(n+1).

%F Sum_{k, 0<=k<=n} T(n-k,k) = A000045(n+2).

%F T(n,k) = A216226(n,k+1).

%e Square array begins:

%e 1, 1, 1, 0, 0, 0, 0, 0, ... row n=0

%e 1, 2, 3, 3, 0, 0, 0, 0, ... row n=1

%e 0, 2, 5, 8, 8, 0, 0, 0, ... row n=2

%e 0, 0, 5, 13, 21, 21, 0, 0, ... row n=3

%e 0, 0, 0, 13, 34, 55, 55, 0, ... row n=4

%e 0, 0, 0, 0, 34, 89, 144, 144, ... row n=5

%e ...

%Y Cf. A000045 (Fibonacci numbers), A001519, A001906, A216226

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Mar 14 2013