A174982 The number of words of length n with 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 or abc.

1, 1, 3, 8, 15, 38, 120, 258, 683, 2116, 4796, 12800, 39094, 91412, 245478, 742376, 1772851, 4779936, 14342766, 34772193, 94010374, 280321572, 687416534, 1862299561, 5524586198, 13670204608, 37092812772, 109567253600, 273104180926, 741976123650, 2183764222716

Offset

0,3

Links

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

Maple

a:= n-> add (add (add (w(na, nb, n-na-nb, t), t=0..2),
             nb=ceil((n-na)/2)..na), na=ceil(n/3)..n):
w:= proc(a, b, c, t) option remember;
      `if`(a=0 and b=0 and c=0, `if`(t=0, 1, 0),
      `if`(a<0 or b<0 or c<0, 0, `if`(t=0, w(a, b-1, c, 0)
      +w(a, b-1, c, 2) +w(a, b, c-1, 0) +w(a, b, c-1, 1),
      `if`(t=1, w(a-1, b, c, 0) +w(a-1, b, c, 1), w(a, b-1, c, 1)))))
    end:
seq (a(n), n=0..40);  # Alois P. Heinz, May 07 2012

Mathematica

a[n_] := Sum[Sum[Sum[w[na, nb, n - na - nb, t], {t, 0, 2}], {nb, Ceiling[(n - na)/2], na}], {na, Ceiling[n/3], n}];
w[a_, b_, c_, t_] := w[a, b, c, t] = If[a == 0 && b == 0 && c == 0, If[t == 0, 1, 0], If[a < 0 || b < 0 || c < 0, 0, If[t == 0, w[a, b - 1, c, 0] + w[a, b - 1, c, 2] + w[a, b, c - 1, 0] + w[a, b, c - 1, 1], If[t == 1, w[a - 1, b, c, 0] + w[a - 1, b, c, 1], w[a, b - 1, c, 1]]]]];
a /@ Range[0, 40] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A176433 A132810 A032159 * A032064 A151397 A369711

Adjacent sequences: A174979 A174980 A174981 * A174983 A174984 A174985

Keyword

nonn

Author

Kusum (k1malik(AT)yahoo.ca), Apr 03 2010

Extensions

a(0) inserted and extended beyond a(15) by Alois P. Heinz, May 07 2012

Status

approved