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A206701
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The number of words of length n created with the letters a,b,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 non adjacent subsequence of letters) of the form cbc.
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2
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1, 1, 3, 9, 17, 46, 114, 262, 574, 1427, 2927, 6603, 14404, 30565, 63613, 138813, 280318, 587475, 1218642, 2483850, 5029611, 10412477, 20733046, 42016631, 84910771, 169447050, 337521488, 680231390, 1340806837, 2667729672, 5306731496, 10458274889, 20608397551
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listen;
history;
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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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EXAMPLE
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a(0) = 1: "".
a(1) = 1: "a".
a(2) = 3: "aa", "ab", "ba".
a(3) = 9: "aaa", "aab", "abc", "acb", "baa", "bac", "bca", "cab", "cba".
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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, 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 and y<>2, w(a, b, c-1, 0, 1), 0))
end:
seq (a(n), n=0..40); # Alois P. Heinz, May 21 2012
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PROG
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sage: def myavoids(w):
....: v = w.count(2)
....: if w.count(1)<v or v<w.count(3):
....: return False
....: return Word([1, 2, 1]).nb_factor_occurrences_in(w)
==0 and Word([3, 2, 3]).nb_subword_occurrences_in(w)==0
....:
sage: for n in range(30):
....: print Words(3, length=n).filter(myavoids).cardinality()
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CROSSREFS
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Cf. A176148, A176354.
Sequence in context: A011755 A128301 A176148 * A176354 A210337 A173140
Adjacent sequences: A206698 A206699 A206700 * A206702 A206703 A206704
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KEYWORD
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nonn
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AUTHOR
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Grazia Barone, Feb 11 2012
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EXTENSIONS
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Extended beyond a(15) by Alois P. Heinz, May 21 2012
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STATUS
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approved
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