A248049 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.

2, 1, 1, 1, 2, 6, 24, 240, 3960, 184800, 33033000, 26125799700, 219429008298500, 31064340573760168675, 206377779224083011749949745, 245390990689739612867279321757020455, 230795626149641527446533813473152766756062242744

Offset

0,1

Comments

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

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

Somos conjectures that log(a(n)) ~ 1.25255*c^n, where c = A060006. - Bill McEachen, Oct 11 2022

Links

Robert Israel, Table of n, a(n) for n = 0..26

Math Stack Exchange, Is OEIS A248049 an Integer Sequence

Formula

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

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

Maple

a[0]:= 2: a[1]:= 1: a[2]:= 1: a[3]:= 1:
for n from 4 to 20 do
a[n] := (a[n-1] + a[n-2]) * (a[n-2] + a[n-3]) / a[n-4]
od:
seq(a[i], i=0..20); # Robert Israel, Mar 18 2020

Prog

(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))};

Crossrefs

Cf. A233522, A060006.

Sequence in context: A179272 A264753 A165680 * A231867 A105685 A228239

Adjacent sequences: A248046 A248047 A248048 * A248050 A248051 A248052

Keyword

nonn

Author

Michael Somos, Sep 30 2014

Status

approved