A169613 - OEIS

%I #18 May 19 2021 16:04:16

%S 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,

%T 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,

%U 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

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

%C Combinatorial limit of row n is essentially A014217.

%e The first 6 rows:

%e 2

%e 1 3

%e 1 2 5

%e 1 2 4 8

%e 1 2 4 6 13

%e 1 2 4 7 10 21

%t 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 *)

%o (Python)

%o from sympy import fibonacci as F, floor

%o def T(n, k): return floor(F(n)/F(n - k))

%o for n in range(3, 16): print([T(n, k) for k in range(1, n - 1)]) # _Indranil Ghosh_, Jul 17 2017

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

%K nonn,tabl

%O 3,1

%A _Clark Kimberling_, Dec 03 2009

%E Offset corrected by _Jean-François Alcover_, Jul 16 2017