cp's OEIS Frontend

A085348 Ratio-determined insertion sequence I(0.264) (see the link below).

%I A085348 #13 Oct 18 2024 20:35:04
%S A085348 1,4,19,72,341,1292,6119,23184,109801,416020,1970299,7465176,35355581,
%T A085348 133957148,634430159,2403763488,11384387281,43133785636,204284540899,
%U A085348 774004377960,3665737348901,13888945017644,65778987739319
%N A085348 Ratio-determined insertion sequence I(0.264) (see the link below).
%C A085348 This is one of the "twin" ratio-determined insertion sequences (RDIS) that are "children" in the next generation below the "parent" sequences I(0.25024) (A004253) and I(0.26816) (A001353) in the recurrence tree of RDIS sequences. The RDIS twin of this sequence is A085349. See the link for an explanation of RDIS twin. See A082630 or A082981 for other recent examples of RDIS sequences.
%C A085348 Assuming that a(n) = 18a(n-2) - a(n-4) is true: For n >= 2, a(n) = (t(i+2n+2) - t(i))/(t(i+n+2) + t(i+n)*(-1)^(n-1)), where (t) is any recurrence of the form (4,1) without regard to initial values. With an additional initional 0 is this sequence the union of A060645 for even n and A049629 for odd n. - _Klaus Purath_, Sep 22 2024
%H A085348 John W. Layman, <a href="http://www.math.vt.edu/people/layman/sequences/ins_seq.htm">Ratio-Determined Insertion Sequences and the Tree of their Recurrence Types</a>, June 2003 [Broken link]
%H A085348 John W. Layman, <a href="/A085376/a085376.txt">Ratio-Determined Insertion Sequences and the Tree of their Recurrence Types</a>, June 2003 [local copy, corrected]
%H A085348 John W. Layman, <a href="https://intranet.math.vt.edu/people/layman/sequences/agedetit.htm">Sequences Generated by Age-Determined Insertion Trees</a>, Jan 2006
%H A085348 John W. Layman, <a href="/A117535/a117535.txt">Sequences Generated by Age-Determined Insertion Trees</a>, Jan 2006 [Local copy]
%F A085348 It appears that a(n)=18a(n-2)-a(n-4).
%F A085348 Apparently a(n)a(n+3) = -4 + a(n+1)a(n+2). - _Ralf Stephan_, May 29 2004
%F A085348 From _Klaus Purath_, Sep 22 2024: (Start)
%F A085348 Assuming that a(n) = 18a(n-2) - a(n-4) is true:
%F A085348 a(2n) = 5a(2n-1) - a(2n-2), n >= 1.
%F A085348 a(2n+1) = 4a(2n) - a(2n-1), n >= 1. (End)
%Y A085348 Cf. A001353, A004253, A082630, A082981, A085349.
%K A085348 nonn
%O A085348 0,2
%A A085348 _John W. Layman_, Jun 24 2003