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 A255706 Number of length-n word structures with no consecutive nonrepeated letters. 2
 1, 1, 1, 4, 11, 38, 151, 655, 3112, 16000, 88285, 519592, 3244512, 21400146, 148530179, 1081222613, 8231314455, 65369494593, 540322688516, 4639020151529, 41295634331020, 380514484523095, 3623898600072459, 35622399584611476, 360965731323718242 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Consider all free words generated over a countably infinite alphabet. Two words are of the same structure provided there is a permutation of the alphabet that sends one word to the other. The number a(n) only counts length-n structures that satisfy the following: For every positive i add(g(n-j)*binomial(n+1-j, j), j=0..(n+1)/2): seq(a(n), n=0..30);  # Alois P. Heinz, Mar 03 2015 MATHEMATICA g[n_] := g[n] = If[n==0, 1, BellB[n-1] - g[n-1]]; a[n_] := Sum[g[n-j] * Binomial[n+1-j, j], {j, 0, (n+1)/2}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 26 2017, after Alois P. Heinz *) PROG (Sage) def a(n): ....words = SetPartitions(range(n)) ....count = len(words) ....for word in words: ........singles = [] ........for letter in word: ........if len(letter)==1: ............singles.append(letter[0]) ........singles.sort() ........for i in range(len(singles) - 1): ............if (singles[i] + 1)==singles[i + 1]: ................count -= 1 ................break ....return count CROSSREFS Cf. A000110, A000296. Sequence in context: A149255 A149256 A149257 * A203161 A050987 A137191 Adjacent sequences:  A255703 A255704 A255705 * A255707 A255708 A255709 KEYWORD nonn AUTHOR Danny Rorabaugh, Mar 02 2015 EXTENSIONS a(11)-a(24) from Alois P. Heinz, Mar 03 2015 STATUS approved

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Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)