A169613 Triangular array: T(n,k)=floor(F(n)/F(n-k)), k=1,2,...,n-2; n>=3, where F=A000045 (Fibonacci numbers).

2, 1, 3, 1, 2, 5, 1, 2, 4, 8, 1, 2, 4, 6, 13, 1, 2, 4, 7, 10, 21, 1, 2, 4, 6, 11, 17, 34, 1, 2, 4, 6, 11, 18, 27, 55, 1, 2, 4, 6, 11, 17, 29, 44, 89, 1, 2, 4, 6, 11, 18, 28, 48, 72, 144, 1, 2, 4, 6, 11, 17, 29, 46, 77, 116, 233, 1, 2, 4, 6, 11, 17, 29, 47, 75, 125, 188, 377, 1, 2, 4, 6, 11

Offset: 3

Author

Clark Kimberling, Dec 03 2009

Keywords

• nonn
• tabl

Comments

Combinatorial limit of row n is essentially A014217.

Examples

			The first 6 rows:
2
1 3
1 2 5
1 2 4 8
1 2 4 6 13
1 2 4 7 10 21
		

Crossrefs

Cf. A000045, A014217, A169614, A169615, A169616.

Programs

Mathematica

T[n_, k_] := Floor[Fibonacci[n]/Fibonacci[n-k]]; Table[T[n, k], {n, 3, 15}, {k, 1, n-2}] // Flatten (* Jean-François Alcover, Jul 16 2017 *)

Python

from sympy import fibonacci as F, floor
def T(n, k): return floor(F(n)/F(n - k))
for n in range(3, 16): print([T(n, k) for k in range(1, n - 1)]) # Indranil Ghosh, Jul 17 2017

Extensions

Offset corrected by Jean-François Alcover, Jul 16 2017