A103516 Triangle read by rows: count in a vee.

1, 2, 2, 3, 0, 3, 4, 0, 0, 4, 5, 0, 0, 0, 5, 6, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 7, 8, 0, 0, 0, 0, 0, 0, 8, 9, 0, 0, 0, 0, 0, 0, 0, 9, 10, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Paul Barry, Feb 09 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A103517, antidiagonal sums are A187012.

Examples

			Triangle begins
1,
2, 2,
3, 0, 3,
4, 0, 0, 4,
5, 0, 0, 0, 5,
6, 0, 0, 0, 0, 6,
7, 0, 0, 0, 0, 0, 7,
8, 0, 0, 0, 0, 0, 0, 8,
...
		

Programs

Mathematica

Join[{1},Flatten[Table[Flatten[Join[{n,PadRight[{},n-2,0],n}]],{n,2,15}]]] (* Harvey P. Dale, Mar 23 2013 *)

PARI

tabl(nn) = {for (i=1, nn, for (j=1, i, if (j == 1, t = i, if (j==i, t = i, t = 0)); print1(t, ", ");); print(););} \\ Michel Marcus, Aug 30 2013

Formula

Number triangle T(n, k)=if(k<=n, 0^(k(n-k))*(n+1), 0)