[seqfan] Re: Trivial array of powers

[Frank Adams-Watters]

This is, of course, what I was hinting at.

As for the linguistics, there are any number of English exclamations that can have a letter repeated 3 (or more) times to represent a prolongation of the sound: eeek, shhh, hmmm, arggg, yesss, nooo, oooh, etc. I don't know of any English words with 3 consecutive letters the same that does not fit this pattern.

I would also cite the story "The Nine Billion Names of God", by Arthur C. Clarke, where one of the restrictions on the names of God is that no letter appears 3 times in a row.

Franklin T. Adams-Watters


-----Original Message-----
From: Richard J. Mathar <mathar at mpia-hd.mpg.de>

In http://list.seqfan.eu/pipermail/seqfan/2015-December/015806.html I was using "alphabet" in the usual sense of combinatorics.  Of course,rejecting only words that have clusters of three or more repeated letters is no longer a "trivial" array, but more like this:
     1      2      3      4      5      6      7     8
     1      4      9     16     25     36     49     64
     0      6     24 60    120    210    336    504
     0     10     66    228    580   1230   2310 3976
     0     16    180    864   2800   7200  15876  31360
     0     26    492   3276  13520  42150 109116 247352
     0     42   1344  12420  65280 246750 749952 1950984
     0     68   3672  47088 315200 1444500 5154408 15388352
 with 2nd column in A006355, 3rd in A121907, 4th in A123620, 5th in A123871 etc.
Richard Mathar_______________________________________________Seqfan Mailing list - http://list.seqfan.eu/