# [seqfan] Re: Trouble with A069726

Paul D Hanna pauldhanna at juno.com
Tue Mar 27 03:34:13 CEST 2012

```Seqfans,
The formulas:
A(x) = 1 - 47*x + 3*x^2 + 3*x*(22-9*x)*A(x) + 9*x*(9*x-2)*A(x)^2 - 81*x^2*A(x)^3
and
a(n) = 3^(n-1)*binomial(3*n, n+1)/(n*(2*n+1)) for n>=1, with a(0)=1
both generate
1, 1, 6, 54, 594, 7371, 99144, 1412802, 21025818, 323686935, 5120138790,
82812679560, 1364498150904, 22839100002036, 387477144862128,

and the above agrees with:
G.f.: A(x) = (1 + 3*y - y^2)/3 where 3*x*y^3 - y + 1=0.
which is a correction to the formula in OEIS:
G.f.: f(x)=(1+3y-y^2)/3 where 3*x^2*y^3-y+1=0.

When compared to the generated terms above to the terms in the OEIS:
1, 1, 6, 54, 594, 7371, 99144, 1412802, 21025818, 323686935, 5120138790,
8281267956,  136449815090,  2283910000203,  38747714486212

it appears that somehow the final digit of the last 4 terms in the OEIS entry got truncated.

Paul

---------- Original Message ----------
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>, Valery Liskovets <liskov at im.bas-net.by>,  Harvey Dale <hpd1 at nyu.edu>, RGWv <rgwv at rgwv.com>
Subject: [seqfan] Trouble with A069726
Date: Mon, 26 Mar 2012 20:42:33 -0400

Dear SeqFans, Valery:

Harvey Dale discovered that something is seriously wrong with A069726.

We have
- a list of 14 or so terms
- a comment relating this to another sequence
- a collection of 3 or 4 formulas

All these things disagree!

Can anyone supply a correct list of terms and some correct
formulas?

I admit the errors are probably all my fault.

Thanks

Neil

--
Dear Friends, I will soon be retiring from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA