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%I #10 Aug 06 2015 20:18:14
%S 1,6,35,204,1188,6919,40295,234672,1366694,7959418,46354440,269961210,
%T 1572213035,9156329637,53325071447,310557107219,1808637367513,
%U 10533228997581,61343923944270,357257684774972,2080614429665859,12117182049311250,70568625653399251
%N Number of n-length words w over a 6-ary alphabet {a_1,...,a_6} such that w contains never more than j consecutive letters a_j (for 1<=j<=6).
%H Geoffrey Critzer and Alois P. Heinz, <a href="/A242629/b242629.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: -(x^6+x^5+x^4+x^3+x^2+x+1) *(x+1)*(x^2-x+1) *(x^2+x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) / (5*x^17 +14*x^16 +32*x^15 +57*x^14 +90*x^13 +123*x^12 +155*x^11 +174*x^10 +181*x^9 +170*x^8 +148*x^7 +114*x^6 +81*x^5 +49*x^4 +26*x^3 +10*x^2 +3*x-1).
%p b:= proc(n, k, c, t) option remember;
%p `if`(n=0, 1, add(`if`(c=t and j=c, 0,
%p b(n-1, k, j, 1+`if`(j=c, t, 0))), j=1..k))
%p end:
%p a:= n-> b(n, 6, 0$2):
%p seq(a(n), n=0..30);
%Y Column k=6 of A242464.
%K nonn,easy
%O 0,2
%A _Geoffrey Critzer_ and _Alois P. Heinz_, May 19 2014
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