Correction for A052944
Rainer Rosenthal
r.rosenthal at web.de
Thu Mar 4 23:18:46 CET 2004
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.
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