A233522 -id:A233522 - cp's OEIS frontend

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

Michael Somos, Sep 30 2014

nonn

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

Robert Israel, Table of n, a(n) for n = 0..26
Math Stack Exchange, Is OEIS A248049 an Integer Sequence

Cf. A233522, A060006.

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

{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))};

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.

A257543 Expansion of 1 / (1 - x^5 - x^8 + x^9) in powers of x.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 1, -1, 1, 0, 0, 2, -2, 1, 1, -2, 4, -3, 1, 3, -6, 7, -3, -2, 9, -13, 11, -1, -11, 22, -23, 12, 10, -33, 46, -35, 2, 43, -78, 81, -37, -41, 122, -159, 118, 4, -162, 281, -277, 114, 167, -443, 558, -391, -52, 610, -1001, 949, -338, -662

Offset: 0

Michael Somos, Apr 28 2015

			G.f. = 1 + x^5 + x^8 - x^9 + x^10 + 2*x^13 - 2*x^14 + x^15 + x^16 + ...

G. C. Greubel, Table of n, a(n) for n = 0..2500
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,0,1,-1).

Cf. A104769, A233522, A247917, A247918.

m:=60; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1 / ((1-x^4)*(1+x^4-x^5)))); // G. C. Greubel, Aug 02 2018

a[ n_] := SeriesCoefficient[ If[ n >= 0, 1 / (1 - x^5 - x^8 + x^9), -x^9 /(1 - x - x^4 + x^9)], {x, 0, Abs@n}];

{a(n) = if( n>=0, polcoeff( 1 / (1 - x^5 - x^8 + x^9) + x * O(x^n), n), polcoeff( -x^9 / (1 - x - x^4 + x^9) + x * O(x^-n), -n))};

G.f.: 1 / ((1 - x^4) * (1 + x^4 - x^5)) = (1 + x) / ((1 + x^3) * (1 - x^4) * (1 + x - x^3)).
a(n) = a(n-5) + a(n-8) - a(n-9) for all n in Z.
a(n) - a(n+2) - a(n+3) has period 12.
a(n) - a(n+12) = A104769(n+5) = -A247917(n+4) for all n in Z.
a(n) + a(n+1) = A247918(n) for all n in Z.
a(n) = -A233522(-9 - n) for all n in Z.

cp's OEIS Frontend

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.

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