login
A217593
Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=1 or if k-n >= 9, T(0,k) = 1 for k = 0..8, 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, 1, 6, 14, 14, 0, 0, 0, 0, 1, 7, 20, 28, 14, 0, 0, 0, 0, 0, 8, 27, 48, 42, 0, 0, 0, 0, 0, 0, 8, 35, 75, 90, 42, 0, 0, 0, 0, 0, 0, 0, 43, 110, 165, 132, 0, 0, 0, 0, 0, 0, 0, 0, 43, 153, 275, 297, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 428, 572, 429, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,8
REFERENCES
A hexagon arithmetic of E. Lucas.
FORMULA
T(n,n) = A033191(n).
T(n,n+1) = A033191(n+1).
T(n,n+2) = A033190(n+1).
T(n,n+3) = A094667(n+1).
T(n,n+4) = A093131(n+1) = A030191(n).
T(n,n+5) = A094788(n+2).
T(n,n+6) = A094825(n+3).
T(n,n+7) = T(n,n+8) = A094865(n+3).
Sum_{k, 0<=k<=n} T(n-k,k) = A178381(n).
EXAMPLE
Square array begins :
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, ...
0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 0, 0, ...
0, 0, 2, 5, 9, 14, 20, 27, 35, 43, 43, 0, 0, ...
0, 0, 0, 5, 14, 28, 75, 110, 153, 196, 196, 0, 0, ....
0, 0, 0, 0, 14, 42, 90, 165, 275, 428, 624, 820, 820, 0, 0, ...
...
Square array, read by rows, with 0 omitted:
1, 1, 1, 1, 1, 1, 1, 1, 1
1, 2, 3, 4, 5, 6, 7, 8, 8
2, 5, 9, 14, 20, 27, 35, 43, 43
5, 14, 28, 48, 75, 110, 153, 196, 196
14, 42, 90, 165, 275, 428, 624, 820, 820
42, 132, 297, 572, 1000, 1624, 2444, 3264, 3264
132, 429, 1001, 2001, 3625, 6069, 9333, 12597, 12597
429, 1430, 3431, 7056, 13125, 22458, 35055, 47652, 47652
...
CROSSREFS
Sequence in context: A216054 A217257 A217315 * A353434 A350529 A322279
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 18 2013
STATUS
approved