cp's OEIS Frontend

A329813 a(n) = denominator(b(n)), where b(0) = b(1) = 1 and b(n) = n*b(n-1)/b(n-2) for n >= 1.

%I A329813 #24 Dec 12 2019 11:39:44
%S A329813 1,1,1,1,1,1,1,2,5,5,7,14,6,15,275,11,91,637,14,200,935,187,247,12103,
%T A329813 245,22,47311,4301,247,112385,5733,2772,1372019,11339,38285,398164,
%U A329813 2184,86394,23324323,56695,21793,69977323,77064,49368,434680565,464899,937099,6018049778,635778,2128995,93977938153
%N A329813 a(n) = denominator(b(n)), where b(0) = b(1) = 1 and b(n) = n*b(n-1)/b(n-2) for n >= 1.
%C A329813 This sequence is derived from a particular case of a general recurrence relation expressed by B(0) = x, B(1) = y and B(n) = n*B(n-1)/B(n-2), for n > 1 and {x,y} any pair of nonzero real numbers. Scatter plots of sequences of this kind exhibit a particular pattern that suggests the following conjecture:
%C A329813 lim_{n->infinity} B(6n+i)/(6n+i) = C_i and C_i != C_j for 0 < i < j < 7.
%C A329813 This means that B(n)/n approaches a cycle of six different constant values which depend on the particular chosen seed {x,y}. In this particular case the seed is {1,1} and the corresponding conjectured constant limits {C_1, C_2, C_3, C_4, C_5, C_6} are approximately {0.431, 0.615, 1.426, 2.319, 1.626, 0.701}. The corresponding constant limits for a generic seed {x,y} are respectively {C_1*y, C_2*y/x, C_3/x, C_4/y, C_5*x/y, C_6*x}. If x and y are not both positive then four of these constants are negative and two are positive.
%F A329813 a(n) = denominator(b(n)), where b(0) = b(1) = 1 and b(n) = n!/Product_{j=1..n-2} a(j), for n > 1.
%t A329813 b[0]=1; b[1]=1;
%t A329813 b[n_]:=b[n]=n*b[n-1]/b[n-2]
%t A329813 (* Table[b[j], {j, 1, 2^10}]//ListPlot *)
%t A329813 Table[Denominator@b[j], {j, 0, 2^5}]
%Y A329813 Cf. A329654 (numerators), A145102, A145103.
%K A329813 nonn,frac
%O A329813 0,8
%A A329813 _Andres Cicuttin_, Nov 21 2019