A114118 Number triangle T(n,k)=sum{j=0..n, C(floor((n+k+j)/3),k)C(k,floor((n+k+j)/3))}.

1, 2, 1, 1, 3, 1, 0, 2, 3, 1, 0, 1, 3, 3, 1, 0, 0, 2, 3, 3, 1, 0, 0, 1, 3, 3, 3, 1, 0, 0, 0, 2, 3, 3, 3, 1, 0, 0, 0, 1, 3, 3, 3, 3, 1, 0, 0, 0, 0, 2, 3, 3, 3, 3, 1, 0, 0, 0, 0, 1, 3, 3, 3, 3, 3, 1, 0, 0, 0, 0, 0, 2, 3, 3, 3, 3, 3, 1, 0, 0, 0, 0, 0, 1, 3, 3, 3, 3, 3, 3, 1, 0, 0, 0, 0, 0, 0, 2, 3, 3, 3, 3, 3, 3, 1

Offset: 0

Author

Paul Barry, Nov 13 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A114119. Diagonal sums are A008619(n+1).

Examples

			Triangle begins
1...........................= 1 = 1 mod 3
2,1.........................= 3 = 0 mod 3
1,3,1.......................= 5 = 2 mod 3
0,2,3,1.....................= 6 = 0 mod 3
0,1,3,3,1...................= 8 = 2 mod 3
0,0,2,3,3,1.................= 9 = 0 mod 3
0,0,1,3,3,3,1...............= 11 = 2 mod 3
0,0,0,2,3,3,3,1.............= 12 = 0 mod 3
0,0,0,1,3,3,3,3,1...........= 14 = 2 mod 3
0,0,0,0,2,3,3,3,3,1.........= 15 = 0 mod 3
0,0,0,0,1,3,3,3,3,3,1.......= 17 = 2 mod 3
0,0,0,0,0,2,3,3,3,3,3,1.....= 18 = 0 mod 3