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A242631 Number of n-length words w over an 8-ary alphabet {a_1,...,a_8} such that w contains never more than j consecutive letters a_j (for 1<=j<=8).

%I A242631 #14 Aug 17 2024 11:10:55
%S A242631 1,8,63,496,3904,30729,241871,1903792,14984945,117948062,928381475,
%T A242631 7307387240,57517205708,452723914009,3563437058402,28048184061555,
%U A242631 220770176730345,1737705044525640,13677657310833723,107658264618591797,847389408675004032,6669890253930098674
%N A242631 Number of n-length words w over an 8-ary alphabet {a_1,...,a_8} such that w contains never more than j consecutive letters a_j (for 1<=j<=8).
%H A242631 Geoffrey Critzer and Alois P. Heinz, <a href="/A242631/b242631.txt">Table of n, a(n) for n = 0..1000</a>
%H A242631 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (5, 16, 39, 79, 144, 229, 345, 480, 631, 782, 927, 1039, 1119, 1148, 1128, 1056, 950, 809, 659, 507, 369, 249, 159, 90, 46, 20, 7).
%F A242631 G.f.: -(x^2+x+1) *(x^6+x^3+1) *(x+1) *(x^2+1) *(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2-x+1) *(x^4+x^3+x^2+x+1) / (7*x^27 +20*x^26 +46*x^25 +90*x^24 +159*x^23 +249*x^22 +369*x^21 +507*x^20 +659*x^19 +809*x^18 +950*x^17 +1056*x^16 +1128*x^15 +1148*x^14 +1119*x^13 +1039*x^12 +927*x^11 +782*x^10 +631*x^9 +480*x^8 +345*x^7 +229*x^6 +144*x^5 +79*x^4 +39*x^3 +16*x^2 +5*x-1).
%p A242631 b:= proc(n, k, c, t) option remember;
%p A242631       `if`(n=0, 1, add(`if`(c=t and j=c, 0,
%p A242631        b(n-1, k, j, 1+`if`(j=c, t, 0))), j=1..k))
%p A242631     end:
%p A242631 a:= n-> b(n, 8, 0$2):
%p A242631 seq(a(n), n=0..30);
%Y A242631 Column k=8 of A242464.
%K A242631 nonn,easy
%O A242631 0,2
%A A242631 _Geoffrey Critzer_ and _Alois P. Heinz_, May 19 2014