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A176433
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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 non adjacent subsequence of letters) of the form abc.
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1
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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
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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MAPLE
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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
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PROG
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(Other) 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 = CountOccurences('a', currentWord); int bCount = CountOccurences('b', currentWord); int cCount = CountOccurences('c', currentWord); if(cCount > bCount) return; if(bCount > aCount) return; currentStrings.Add(currentWord); } } private static int CountOccurences(char ch, string word) { int rez = 0; for(int i = 0 ; i < word.Length; i ++) if (word == ch) rez++; return rez; }
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CROSSREFS
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Sequence in context: A032234 A032255 A137475 * A132810 A032159 A174982
Adjacent sequences: A176430 A176431 A176432 * A176434 A176435 A176436
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KEYWORD
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nonn
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AUTHOR
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Patrick McQuade (patrick.mcquade(AT)peelsb.com), Apr 17 2010
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EXTENSIONS
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More terms from Alois P. Heinz, May 22 2012
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STATUS
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approved
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