(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 re: Solution by Jer)

1
1  1
1  2
1  3  1
1  4  3
1  5  6  1
1  6 10  4
1  7 15 10  1
1  8 21 20  5
1  9 28 35 15 1

claims that for a 3-letter alphabet there is only 1 2-letter word, but there are actually 2: ac and ca. For a 4-letter alphabet it says there are 3 words of 2 letters, but there are 6: ac, ca, ad, da, bd, db. It lists no 3-letter words for the 4-letter alphabet, though there are 4: adb, bda, cad, dac.

My own table (more forthcoming in another post) looks like:

1      1  1                                      
2      1  2   0                                   
3      1  3   2    0                               
4      1  4   6    4    2                          
5      1  5  12   18   20    14                    
6      1  6  20   48   90   124    90              
7      1  7  30  100  272   582   860   646        
8      1  8  42  180  650  1928  4386  6748  5242

 

Posted by Charlie on 2014-03-25 15:39:29