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

%I A169613 #18 May 19 2021 16:04:16
%S A169613 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 A169613 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 A169613 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 A169613 Triangular array: T(n,k)=floor(F(n)/F(n-k)), k=1,2,...,n-2; n>=3, where F=A000045 (Fibonacci numbers).
%C A169613 Combinatorial limit of row n is essentially A014217.
%e A169613 The first 6 rows:
%e A169613 2
%e A169613 1 3
%e A169613 1 2 5
%e A169613 1 2 4 8
%e A169613 1 2 4 6 13
%e A169613 1 2 4 7 10 21
%t A169613 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 A169613 (Python)
%o A169613 from sympy import fibonacci as F, floor
%o A169613 def T(n, k): return floor(F(n)/F(n - k))
%o A169613 for n in range(3, 16): print([T(n, k) for k in range(1, n - 1)]) # _Indranil Ghosh_, Jul 17 2017
%Y A169613 Cf. A000045, A014217, A169614, A169615, A169616.
%K A169613 nonn,tabl
%O A169613 3,1
%A A169613 _Clark Kimberling_, Dec 03 2009
%E A169613 Offset corrected by _Jean-François Alcover_, Jul 16 2017