A176433 The number of words of length n created with letters a, b, and c with at least as many a's as b's and at least as many b's as c's and no adjacent letters forming the pattern aba and no subwords (any adjacent or nonadjacent subsequence of letters) of the form abc.

1, 1, 3, 8, 15, 35, 96, 186, 419, 1035, 2021, 4353, 10171, 19721, 41466, 93118, 180018, 371539, 813425, 1566398, 3194133, 6859558, 13179004, 26617619, 56371355, 108060479, 216736146, 453947049, 868857655, 1732792511, 3598157885, 6877348410, 13655273038

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Maple

a:= n-> add(add(w(na, nb, n-na-nb, 0, 0),
        nb=ceil((n-na)/2)..min(n-na, na)), na=ceil(n/3)..n):
w:= proc(a, b, c, x, y) option remember;
      `if`([a, b, c]=[0$3], 1,
      `if`(a>0 and x<2 and y<2, w(a-1, b, c, 1, y), 0)+
      `if`(b>0, w(a, b-1, c, `if`(x=1, 2, 0), `if`(y>0, 2, 0)), 0)+
      `if`(c>0, w(a, b, c-1, 0, `if`(y=0, 1, y)), 0))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, May 22 2012

Mathematica

a[n_] := Sum[Sum[w[na, nb, n - na - nb, 0, 0], {nb, Ceiling[(n - na)/2], Min[n - na, na]}], {na, Ceiling[n/3], n}];
w[a_, b_, c_, x_, y_] := w[a, b, c, x, y] =
  If[{a, b, c} == {0, 0, 0}, 1,
  If[a > 0 && x < 2 && y < 2, w[a - 1, b, c, 1, y], 0] +
  If[b > 0, w[a, b - 1, c, If[x == 1, 2, 0], If[y > 0, 2, 0]], 0] +
  If[c > 0, w[a, b, c - 1, 0, If[y == 0, 1, y]], 0]];
a /@ Range[0, 40] (* Jean-François Alcover, Nov 20 2020, after Alois P. Heinz *)

Prog

(C#) private static void GenerateCombo(string currentWord, int maxLength, ICollection<string> currentStrings) { if (currentWord.Length < maxLength) { GenerateCombo(currentWord+"a", maxLength, currentStrings); GenerateCombo(currentWord+"b", maxLength, currentStrings); GenerateCombo(currentWord+"c", maxLength, currentStrings); } else { if (Regex.IsMatch(currentWord, "aba")) return; if (Regex.IsMatch(currentWord, "[abc]*a[abc]*b[abc]*c[abc]*")) return; int aCount = CountOccurrences('a', currentWord); int bCount = CountOccurrences('b', currentWord); int cCount = CountOccurrences('c', currentWord); if(cCount > bCount) return; if(bCount > aCount) return; currentStrings.Add(currentWord); } } private static int CountOccurrences(char ch, string word) { int rez = 0; for(int i = 0 ; i < word.Length; i ++) if (word == ch) rez++; return rez; }

Crossrefs

Sequence in context: A032234 A032255 A137475 * A132810 A032159 A174982

Adjacent sequences: A176430 A176431 A176432 * A176434 A176435 A176436

Keyword

nonn

Author

Patrick McQuade (patrick.mcquade(AT)peelsb.com), Apr 17 2010

Extensions

More terms from Alois P. Heinz, May 22 2012

Status

approved