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

3,1

Comments

Combinatorial limit of row n is essentially A014217.

Links

Table of n, a(n) for n=3..85.

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A257912 A036262 A080521 * A176572 A168017 A293980

Adjacent sequences: A169610 A169611 A169612 * A169614 A169615 A169616

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 03 2009

Extensions

Offset corrected by Jean-François Alcover, Jul 16 2017

Status

approved