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A217770
Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=4 or if k-n >= 6, T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
6
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 0, 1, 5, 10, 10, 4, 0, 0, 6, 15, 20, 14, 0, 0, 0, 6, 21, 35, 34, 14, 0, 0, 0, 0, 27, 56, 69, 48, 0, 0, 0, 0, 0, 27, 83, 125, 117, 48, 0, 0, 0, 0, 0, 0, 110, 208, 242, 165, 0, 0, 0, 0, 0, 0, 0, 110, 318, 450, 407, 165
OFFSET
0,5
COMMENTS
A hexagon arithmetic of E. Lucas.
FORMULA
T(n,n+4) = T(n,n+5) = A094788(n+2).
T(n,n+3) = A217783(n).
T(n,n+2) = A217779(n).
T(n,n+1) = A081567(n).
T(n,n) = A217782(n).
T(n+1,n) = A217778(n).
T(n+3,n) = T(n+2,n) = A094667(n+1).
Sum(T(n-k,k), k=0..n) = A217777(n).
EXAMPLE
Square array begins:
n=0: 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...
n=1: 1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, 0, ...
n=2: 1, 3, 6, 10, 15, 21, 27, 27, 0, 0, 0, 0, ...
n=3: 1, 4, 10, 20, 35, 56, 83, 110, 110, 0, 0, 0, ...
n=4: 0, 4, 14, 34, 69, 125, 208, 318, 428, 428, 0, 0, ...
n=5: 0, 0, 14, 48, 117, 242, 450, 768, 1196, 1624, 1624, 0, ...
...
Square array, read by rows, with 0 omitted:
...1, 1, 1, 1, 1, 1
...1, 2, 3, 4, 5, 6, 6
...1, 3, 6, 10, 15, 21, 27, 27
...1, 4, 10, 20, 35, 56, 83, 110, 110
...4, 14, 34, 69, 125, 208, 318, 428, 428
..14, 48, 117, 242, 450, 768, 1196, 1624, 1624
..48, 165, 407, 857, 1625, 2821, 4445, 6069, 6069
.165, 572, 1429, 3054, 5875, 10320, 16389, 22458, 22458
.572, 2001, 5055, 10930, 21250, 37639, 60097, 82555, 82555
2001, 7056, 17986, 39236, 76875, 136972, 219527, 302082, 302082
...
Triangle begins:
1
1, 1
1, 2, 1
1, 3, 3, 1
1, 4, 6, 4, 0
1, 5, 10, 10, 4, 0
0, 6, 15, 20, 14, 0, 0
0, 6, 21, 35, 34, 14, 0, 0
...
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 24 2013
STATUS
approved