(D3)How many subsets of (a,b,c, … x,y,z) contain no letters neighboring each other in the English ABC (26 letters)?

(D4)How many "words" (i.e, ordered subsets from (a,b,c, … x,y,z)) contain no neighboring letters that neighbor each other in the English ABC (26 letters)?

(In reply to solution to part 1; thoughts on part 2 by Charlie)

Part 1 is easy.

Part 2 is a D4 question, to which I do not have an "official solution". Since you show a procedure leading to a final answer and it is limited only by size I suggest that you provide 2 "modified"  answers:

1. Part 2 - an exact answer , applied to Hawaian alphabet.

2. Part 2 - an  answer re English ABC, providing intelligent apprroximation (like log a(26).

IMHO - the result of part 2 qualifies to give you credit in OEIS, - the table does not need to reach big-big numbers.

 

Posted by Ady TZIDON on 2014-03-26 02:25:38