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A217257
Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 7, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,3) = T(0,4) = T(0,5) = T(0,6) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
3
1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 5, 0, 0, 0, 1, 5, 9, 5, 0, 0, 0, 0, 6, 14, 14, 0, 0, 0, 0, 0, 6, 20, 28, 14, 0, 0, 0, 0, 0, 0, 26, 48, 42, 0, 0, 0, 0, 0, 0, 0, 26, 74, 90, 42, 0, 0, 0, 0, 0, 0, 0, 0, 100, 164, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 264, 296, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364, 560, 428, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,8
COMMENTS
A hexagon arithmetic of E. Lucas.
REFERENCES
E. Lucas, Théorie des nombres, A. Blanchard, Paris, 1958, p.89
LINKS
E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, p. 89
FORMULA
T(n,n) = A024175(n).
T(n,n+1) = A024175(n+1).
T(n,n+2) = A094803(n+1).
T(n,n+3) = A007070(n).
T(n,n+4) = A094806(n+2).
T(n,n+5) = T(n,n+6) = A094811(n+2).
Sum_{k, 0<=k<=n} T(n-k,k) = A030436(n).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=0
0, 1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=1
0, 0, 2, 5, 9, 14, 20, 26, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=2
0, 0, 0, 5, 14, 28, 48, 74, 100, 100, 0, 0, 0, 0, 0, 0, 0, ... row n=3
0, 0, 0, 0, 14, 42, 90, 162, 264, 364, 364, 0, 0, 0, 0, 0, ... row n=4
0, 0, 0, 0, 0, 42, 132, 296, 560, 924, 1288, 1288, 0, 0, 0, ... row n=5
...
CROSSREFS
Cf. similar sequences: A216230, A216228, A216226, A216238, A216054.
Sequence in context: A157608 A220062 A216054 * A217315 A217593 A353434
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 17 2013
EXTENSIONS
a(69) = 0 deleted by Georg Fischer, Oct 16 2021
STATUS
approved