cp's OEIS Frontend

A242632 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).

%I A242632 #11 Aug 17 2024 11:12:25
%S A242632 1,9,80,711,6318,56143,498896,4433274,39394819,350068993,3110771999,
%T A242632 27642843622,245638961566,2182789161071,19396631915857,
%U A242632 172361736254288,1531635402139359,13610370004776711,120944038906506659,1074729088326395697,9550223588843166996
%N A242632 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 A242632 Geoffrey Critzer and Alois P. Heinz, <a href="/A242632/b242632.txt">Table of n, a(n) for n = 0..1000</a>
%H A242632 <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 A242632 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 A242632 b:= proc(n, k, c, t) option remember;
%p A242632       `if`(n=0, 1, add(`if`(c=t and j=c, 0,
%p A242632        b(n-1, k, j, 1+`if`(j=c, t, 0))), j=1..k))
%p A242632     end:
%p A242632 a:= n-> b(n, 9, 0$2):
%p A242632 seq(a(n), n=0..30);
%Y A242632 Column k=9 of A242464.
%K A242632 nonn,easy
%O A242632 0,2
%A A242632 _Geoffrey Critzer_ and _Alois P. Heinz_, May 19 2014