|
%I #9 Aug 06 2015 20:19:56
%S 1,9,80,711,6318,56143,498896,4433274,39394819,350068993,3110771999,
%T 27642843622,245638961566,2182789161071,19396631915857,
%U 172361736254288,1531635402139359,13610370004776711,120944038906506659,1074729088326395697,9550223588843166996
%N Number of n-length words w over a 9-ary alphabet {a_1,...,a_9} such that w contains never more than j consecutive letters a_j (for 1<=j<=9).
%H Geoffrey Critzer and Alois P. Heinz, <a href="/A242632/b242632.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: -(x+1) *(x^4-x^3+x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+x+1) *(x^6+x^3+1) *(x^2+1)*(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2-x+1) / (8*x^31 +15*x^30 +38*x^29 +66*x^28 +118*x^27 +179*x^26 +273*x^25 +371*x^24 +503*x^23 +628*x^22 +775*x^21 +895*x^20 +1023*x^19 +1099*x^18 +1167*x^17 +1172*x^16 +1161*x^15 +1087*x^14 +1007*x^13 +875*x^12 +754*x^11 +606*x^10 +483*x^9 +352*x^8 +258*x^7 +166*x^6 +109*x^5 +59*x^4 +34*x^3 +12*x^2 +7*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, 9, 0$2):
%p seq(a(n), n=0..30);
%Y Column k=9 of A242464.
%K nonn,easy
%O 0,2
%A _Geoffrey Critzer_ and _Alois P. Heinz_, May 19 2014
|
