From BRYAN@wvnvm.wvnet.edu Wed Aug 24 23:07:21 1994
Return-Path:
Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA07590; Wed, 24 Aug 94 23:07:21 EDT
Message-Id: <9408250307.AA07590@life.ai.mit.edu>
Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2)
with BSMTP id 1861; Wed, 24 Aug 94 23:06:53 EDT
Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU
(LMail V1.2a/1.8a) with BSMTP id 6531; Wed, 24 Aug 1994 23:06:53 -0400
X-Acknowledge-To:
Date: Wed, 24 Aug 1994 23:06:52 EDT
From: "Jerry Bryan"
To: "der Mouse" ,
"Cube Lovers List"
Subject: Re: Updated Upper Limits, Q-turns
In-Reply-To: Message of 08/21/94 at 06:33:02 from ,
mouse@collatz.mcrcim.mcgill.edu
On 08/21/94 at 06:33:02 der Mouse said:
>> Dan's recursion formula is:
>>> P[n] <= 4*2*P[n-1] + 6*2*P[n-2] + 4*2*P[n-3] + 1*2*P[n-4]
>> Dan's calculations:
>>> P[0] = 1
>>> P[1] = 12
>>> P[2] = 114
>>> P[3] = 1,068
>>> P[4] = 10,011
>Ummm. 4*2*P[4-1] + 6*2*P[4-2] + 4*2*P[4-3] + 1*2*P[4-4] =
> 4*2*1068 + 6*2*114 + 4*2*12 + 1*2*1 = 10010 < P[4].
>What have I missed? Is Dan's formula not valid until n=5 or something?
I just rechecked Dan's original note of 9 January 1981. He specifically
says the formula is good for n > 4. Mea culpa. However, I still do
not fully understand *why* this should be the case.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan) (304) 293-5192
Associate Director, WVNET (304) 293-5540 fax
837 Chestnut Ridge Road BRYAN@WVNVM
Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU
If you don't have time to do it right today, what makes you think you are
going to have time to do it over again tomorrow?