A094570 Triangle T(n,k) read by rows: T(n,k) = F(k) + F(n-k) where F(n) is the n-th Fibonacci number.

0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 5, 4, 3, 3, 4, 5, 8, 6, 4, 4, 4, 6, 8, 13, 9, 6, 5, 5, 6, 9, 13, 21, 14, 9, 7, 6, 7, 9, 14, 21, 34, 22, 14, 10, 8, 8, 10, 14, 22, 34, 55, 35, 22, 15, 11, 10, 11, 15, 22, 35, 55, 89, 56, 35, 23, 16, 13, 13, 16, 23, 35, 56, 89, 144, 90, 56, 36, 24, 18, 16, 18, 24, 36, 56, 90, 144

Offset: 0

Author

Clark Kimberling, May 12 2004

Keywords

• nonn
• tabl

Examples

			Triangle begins:
0;
1, 1;
1, 2, 1;
2, 2, 2, 2;
3, 3, 2, 3, 3;
5, 4, 3, 3, 4, 5;
8, 6, 4, 4, 4, 6, 8;
13, 9, 6, 5, 5, 6, 9, 13;
21, 14, 9, 7, 6, 7, 9, 14, 21;
		

Links

• Reinhard Zumkeller, Rows n=0..125 of triangle, flattened

Crossrefs

Cf. A000045, A000071, A006355, A141169.

Programs

PARI

row(n) = vector(n+1, k, k--; fibonacci(k)+fibonacci(n-k)); \\ Michel Marcus, Mar 22 2021

Formula

Row n: F(0)+F(n), F(1)+F(n-1), F(2)+F(n-2), ..., F(n-1)+F(1), F(n)+F(0).

From Reinhard Zumkeller, Mar 21 2011: (Start)

T(n,0) = T(n,n) = A000045(n).

T(2*n,n) = A006355(n+1).

T(n,k) = A141169(n,k) + A141169(n,n-k). (End)

Sum(T(n,k), 0<=k<=n) = 2*A000071(n+2) = 2*A000045(n+2) - 2. - Philippe Deléham, Apr 07 2013