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 A206701 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 nonadjacent subsequence of letters) of the form cbc. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 EXAMPLE 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". G.f. = 1 + x + 3*x^2 + 9*x^3 + 17*x^4 + 46*x^5 + 114*x^6 + 262*x^7 + ... 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, 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 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, 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 && y != 2, w[a, b, c - 1, 0, 1], 0]]; a /@ Range[0, 40] (* Jean-François Alcover, Nov 12 2020, after Alois P. Heinz *) PROG (Sage) def myavoids(w):     v = w.count(2)     if w.count(1)

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)