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A216235
Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 2 or if k-n >= 5, 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).
4
1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 1, 4, 5, 0, 0, 0, 5, 9, 5, 0, 0, 0, 5, 14, 14, 0, 0, 0, 0, 0, 19, 28, 14, 0, 0, 0, 0, 0, 19, 47, 42, 0, 0, 0, 0, 0, 0, 0, 66, 89, 42, 0, 0, 0, 0, 0, 0, 0, 66, 155, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 286, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 507, 417, 0, 0, 0, 0, 0, 0
OFFSET
0,5
COMMENTS
Arithmetic hexagon of E. Lucas.
LINKS
E. Lucas, Théorie des nombres, Gauthier-Villars, Paris 1891, Tome 1, p. 89.
FORMULA
T(n,n) = T(n+1,n) = A080937(n+1).
T(n,n+1) = A094790(n+1).
T(n,n+2) = A094789(n+1).
T(n,n+3) = T(n,n+4) = A005021(n).
Sum_{k=0..n} T(n-k,k) = A028495(n+1). - Philippe Deléham, Mar 23 2013
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, ... row n=0
1, 2, 3, 4, 5, 5, 0, 0, 0, 0, ... row n=1
0, 2, 5, 9, 14, 19, 19, 0, 0, 0, ... row n=2
0, 0, 5, 14, 28, 47, 66, 66, 0, 0, ... row n=3
0, 0, 0, 14, 42, 89, 155, 221, 221, 0, ... row n=4
0, 0, 0, 0, 42, 131, 286, 507, 728, 728, ... row n=5
...
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 14 2013
STATUS
approved