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Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=5 or if k-n>=5, T(4,0) = T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
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%I #7 Mar 14 2013 20:49:45

%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,0,5,10,10,5,0,0,5,15,20,15,5,0,0,0,20,

%T 35,35,20,0,0,0,0,20,55,70,55,20,0,0,0,0,0,75,125,125,75,0,0,0,0,0,0,

%U 75,200,250,200

%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=5 or if k-n>=5, T(4,0) = T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

%F T(n,n) = A147748(n).

%F T(n+1,n) = T(n,n+1) = A081567(n).

%F T(n+2,n) = T(n,n+2) = A039717(n+1).

%F T(n+3,n) = T(n+4,n) = T(n,n+3) = T(n,n+4) = A030191(n).

%F Sum_{k, 0<=k<=n} T(n-k,k) = A068913(4,n) = A216212(n).

%e Square array begins:

%e 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...

%e 1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, ...

%e 1, 3, 6, 10, 15, 20, 20, 0, 0, 0, 0, ...

%e 1, 4, 10, 20, 35, 55, 75, 75, 0, 0, 0, ...

%e 1, 5, 15, 35, 70, 125, 200, 275, 275, 0, 0, ...

%e 0, 5, 20, 55, 125, 250, 450, 725, 1000, 1000, 0, ...

%e 0, 0, 20, 75, 200, 450, 900, ...

%Y Cf. A030191, A039717, A068913, A081567, A147748, A216210, A216212, A216218

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Mar 13 2013