Date: Wed, 24 Aug 94 23:06:52 -0400 (EDT)
From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
Subject: Re: Updated Upper Limits, Q-turns
```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?