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A216220
Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=4, T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
8
1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 0, 4, 5, 0, 0, 0, 4, 9, 5, 0, 0, 0, 0, 13, 14, 0, 0, 0, 0, 0, 13, 27, 14, 0, 0, 0, 0, 0, 0, 40, 41, 0, 0, 0, 0, 0, 0, 0, 40, 81, 41, 0, 0, 0, 0, 0, 0, 0, 0, 121, 122, 0, 0, 0, 0, 0
OFFSET
0,5
COMMENTS
T(0,2), T(1,1), T(1,2), T(1,3), ... T(n,n), T(n,n+1), T(n,n+2), ... is the sequence A140298.
FORMULA
T(n,n) = T(n+1,n) = A007051(n).
T(n,n+1) = 3^n = A000244(n).
T(n,n+2) = T(n,n+3) = A003462(n+1).
Sum_{k, 0<=k<=n} T(n-k,k) = A038754(n).
EXAMPLE
Square array begins:
1, 1, 1, 1, 0, 0, 0, 0, 0, ...
1, 2, 3, 4, 4, 0, 0, 0, 0, ...
0, 2, 5, 9, 13, 13, 0, 0, 0, ...
0, 0, 5, 14, 27, 40, 40, 0, 0, ...
0, 0, 0, 14, 41, 81, 121, 121, 0, ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 13 2013
STATUS
approved