Correction for A052944

[Rainer Rosenthal]

Please let me forward a correction I received in de.sci.mathematik
from Hermann Kremer, when I tolf them about A052944.

I think he will be right (as nearly always), but I just wanted to
ask here.

Best regards
Rainer Rosenthal
r.rosenthal at web.de

:   ID Number: A052944
:   URL:       http://www.research.att.com/projects/OEIS?Anum=A052944
:   Sequence:  0,2,5,10,19,36,69,134,263,520,1033,2058,4107,8204,16397,
:            32782,65551,131088,262161,524306,1048595,2097172,4194325,
:            8388630,16777239,33554456,67108889,134217754,268435483,
:            536870940,1073741853,2147483678
:   Name:      a(n) = 2^n + n - 1
:   G.f.: (-2+3*x)/(-1+2*x)/(-1+x)^2

The G.f. is OK  ...

:   Recurrence: {a(1)=5,a(0)=2,2*a(n)-a(n+1)+1-n}

But not the recursion, which should read

    { a(0)=0, a(1)=2, a(2)=5,  a(n+3) = 4*a(n+2) - 5*a(n+1) + 2*a(n) }

if the sequence begins with n = 0.

a(3) =  4*5 -  5*2 +  2*0 = 10
a(4) = 4*10 -  5*5 +  2*2 = 19
a(5) = 4*19 - 5*10 +  2*5 =  36
a(6) = 4*36 - 5*19 + 2*10 =  69
etc.