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?