%I #11 Aug 17 2024 11:12:25

%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>

%H <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (7, 12, 34, 59, 109, 166, 258, 352, 483, 606, 754, 875, 1007, 1087, 1161, 1172, 1167, 1099, 1023, 895, 775, 628, 503, 371, 273, 179, 118, 66, 38, 15, 8).

%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