A248049 - OEIS

%I #33 Oct 12 2022 15:21:36

%S 2,1,1,1,2,6,24,240,3960,184800,33033000,26125799700,219429008298500,

%T 31064340573760168675,206377779224083011749949745,

%U 245390990689739612867279321757020455,230795626149641527446533813473152766756062242744

%N a(n) = (a(n-1) + a(n-2)) * (a(n-2) + a(n-3)) / a(n-4) with a(0) = 2, a(1) = a(2) = a(3) = 1.

%C It seems that degrees of factors when using [2,1,1,y] as initial condition are given by A233522. - _F. Chapoton_, May 21 2020

%C It seems also that degrees (w.r.t. x) of factors when using [2,1,x,y] as initial condition are given by A247907. - _F. Chapoton_, Jan 03 2021

%C Somos conjectures that log(a(n)) ~ 1.25255*c^n, where c = A060006. - _Bill McEachen_, Oct 11 2022

%H Robert Israel, <a href="/A248049/b248049.txt">Table of n, a(n) for n = 0..26</a>

%H Math Stack Exchange, <a href="https://math.stackexchange.com/questions/3586309/is-oeis-a248049-an-integer-sequence/4004892#4004892">Is OEIS A248049 an Integer Sequence</a>

%F a(n) = a(4-n) for all n in Z.

%F a(n) * a(n+4) = (a(n+1) + a(n+2)) * (a(n+2) + a(n+3)) for all n in Z.

%p a[0]:= 2: a[1]:= 1: a[2]:= 1: a[3]:= 1:

%p for n from 4 to 20 do

%p a[n] := (a[n-1] + a[n-2]) * (a[n-2] + a[n-3]) / a[n-4]

%p od:

%p seq(a[i],i=0..20); # _Robert Israel_, Mar 18 2020

%o (PARI) {a(n) = if( n<0, n=4-n); if( n<4, (n==0)+1, (a(n-1) + a(n-2)) * (a(n-2) + a(n-3)) / a(n-4))};

%Y Cf. A233522, A060006.

%K nonn

%O 0,1

%A _Michael Somos_, Sep 30 2014