A217765 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=3 or if k-n >= 6, 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).

1, 1, 1, 1, 2, 1, 1, 3, 3, 0, 1, 4, 6, 3, 0, 1, 5, 10, 9, 0, 0, 0, 6, 15, 19, 9, 0, 0, 0, 6, 21, 34, 28, 0, 0, 0, 0, 0, 27, 55, 62, 28, 0, 0, 0, 0, 0, 27, 82, 117, 90, 0, 0, 0, 0, 0, 0, 0, 109, 199, 207, 90, 0, 0, 0, 0, 0, 0, 0, 109, 308, 406, 297, 0, 0, 0, 0

Offset: 0

Author

Philippe Deléham, Mar 24 2013

Keywords

• nonn
• tabl

Comments

A hexagon arithmetic of E. Lucas.

Examples

			Square array begins:
1, 1, 1, 1, 1, 1, 0, 0, 0, ... row n=0
1, 2, 3, 4, 5, 6, 6, 0, 0, ... row n=1
1, 3, 6, 10, 15, 21, 27, 27, 0, 0, ... row n=2
0, 3, 9, 19, 34, 55, 82, 109, 109, 0, 0, ... row n=3
0, 0, 9, 28, 62, 117, 199, 308, 417, 417, 0, 0, ... row n=4
0, 0, 0, 28, 90, 207, 406, 714, 1131, 1548, 1548, 0, 0, ... row n=5
...
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
3, 9, 19, 34, 55, 82, 109, 109
9, 28, 62, 117, 199, 308, 417, 417
28, 90, 207, 406, 714, 1131, 1548, 1548
90, 297, 703, 1417, 2548, 4096, 5644, 5644
297, 1000, 2417, 4965, 9061, 14705, 20349, 20349
1000, 3417, 8382, 17443, 32148, 52497, 72846, 72846
3417, 11799, 29242, 61390, 113887, 186733, 259579, 259579
11799, 41041, 102431, 216318, 403051, 662630, 922209, 922209
...
		

Crossrefs

Cf. Similar sequences: A216201, A216210, A216216, A216218, ...

Formula

T(n,n+4) = T(n,n+5) = A094829(n+2).

T(n,n+3) = A094834(n+1).

T(n,n+2) = A094833(n+1).

T(n,n+1) = A094832(n).

T(n,n) = A094831(n).

T(n+1,n) = T(n+2,n) = A094826(n).

sum(T(n-k,k), 0<=k<=n) = A065455(n).