login
A216232
Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 3 or if k-n >= 5, 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).
7
1, 1, 1, 1, 2, 1, 1, 3, 3, 0, 1, 4, 6, 3, 0, 0, 5, 10, 9, 0, 0, 0, 5, 15, 19, 9, 0, 0, 0, 0, 20, 34, 28, 0, 0, 0, 0, 0, 20, 54, 62, 28, 0, 0, 0, 0, 0, 0, 74, 116, 90, 0, 0, 0, 0, 0, 0, 0, 74, 190, 206, 90, 0, 0, 0, 0, 0, 0, 0, 0, 264, 396, 296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 660, 692, 296, 0, 0, 0, 0, 0
OFFSET
0,5
COMMENTS
Arithmetic hexagon of E. Lucas.
REFERENCES
E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome 1, p. 89.
LINKS
E. Lucas, Théorie des nombres, Gauthier-Villars, Paris 1891, Tome 1, p. 89.
FORMULA
T(n,n) = A094817(n), for n > 0.
T(n+1,n) = T(n+2,n) = A094803(n).
T(n,n+1) = A007052(n).
T(n,n+2) = A094821(n+1).
T(n,n+3) = T(n,n+4) = A094806(n).
Sum_{k=0..n} T(n-k,k) = A217730(n). - Philippe Deléham, Mar 22 2013
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ... row n=0
1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, ... row n=1
1, 3, 6, 10, 15, 20, 20, 0, 0, 0, 0, ... row n=2
0, 3, 9, 19, 34, 54, 74, 74, 0, 0, 0, ... row n=3
0, 0, 9, 28, 62, 116, 190, 264, 264, 0, 0, ... row n=4
0, 0, 0, 28, 90, 206, 396, 660, 924, 924, 0, ... row n=5
...
Array, read by rows, with 0 omitted:
1, 1, 1, 1, 1
1, 2, 3, 4, 5, 5
1, 3, 6, 10, 15, 20, 20
3, 9, 19, 34, 54, 74, 74
9, 28, 62, 116, 190, 264, 264
28, 90, 206, 396, 660, 924, 924
90, 296, 692, 1352, 2276, 3200, 3200
...
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 14 2013
STATUS
approved