A123265 Fibonacci-Lucas triangle read by rows.

2, 1, 2, 3, 3, 2, 4, 8, 5, 2, 7, 15, 15, 7, 2, 11, 30, 35, 24, 9, 2, 18, 56, 80, 66, 35, 11, 2, 29, 104, 171, 170, 110, 48, 13, 2, 47, 189, 355, 407, 315, 169, 63, 15, 2, 76, 340, 715, 932, 832, 532, 245, 80, 17, 2

Offset: 0

Author

Philippe Deléham, Nov 07 2006

Keywords

• nonn
• tabl

Comments

As a Riordan array, this is ((2-x)/(1-x-x^2),x/(1-x-x^2)) . Row sums form A078343, diagonals sums form A014551.

Examples

			Triangle begins:
2;
1, 2;
3, 3, 2;
4, 8, 5, 2;
7, 15, 15, 7, 2;
11, 30, 35, 24, 9, 2;
18, 56, 80, 66, 35, 11, 2;
29, 104, 171, 170, 110, 48, 13, 2;
		

Crossrefs

Cf. A000032, A099920 ; A007395, A005408, A005563.

Formula

T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-2,k), T(0,0)=2, T(1,0)=1, T(n,k)=0 if k<0 or if k>n . T(n,0)=L(n)=A000032(n),Lucas numbers.