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

0,1

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.

Links

Table of n, a(n) for n=0..54.

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.

Example

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.

Sequence in context: A230128 A342095 A340828 * A104345 A244516 A363264

Adjacent sequences: A123262 A123263 A123264 * A123266 A123267 A123268

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 07 2006

Status

approved