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A216218
Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=2, T(1,0) = T(0,0) = T(0,1) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
11
1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,5
COMMENTS
With zeros omitted, this is A173862.
FORMULA
T(n,n) = T(n+1,n) = T(n,n+1) = 2^n = A000079(n).
Sum_{k, 0<=k<=n} T(n-k,k) = A016116(n+1) = A163403(n+1).
EXAMPLE
Square array begins:
1, 1, 0, 0, 0, 0, 0, 0, ... row n=0
1, 2, 2, 0, 0, 0, 0, 0, ... row n=1
0, 2, 4, 4, 0, 0, 0, 0, ... row n=2
0, 0, 4, 8, 8, 0, 0, 0, ... row n=3
0, 0, 0, 8, 16, 16, 0, 0, ... row n=4
0, 0, 0, 0, 16, 32, 32, 0, ... row n=5
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 13 2013
STATUS
approved