cp's OEIS Frontend

A249019 Number of ternary words of length n in which all digits 0..2 occur in every 6 consecutive digits.

%I A249019 #21 Nov 11 2024 22:23:10
%S A249019 1,3,9,27,81,243,540,1440,3804,9960,25908,67344,175884,458832,1196364,
%T A249019 3119304,8134164,21212832,55316892,144249168,376159644,980918904,
%U A249019 2557958964,6670420704,17394543180,45359994336,118285895244,308455762488,804364332180,2097551985168,5469815336796,14263713072192
%N A249019 Number of ternary words of length n in which all digits 0..2 occur in every 6 consecutive digits.
%H A249019 Colin Barker, <a href="/A249019/b249019.txt">Table of n, a(n) for n = 0..1000</a>
%H A249019 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,3,5,6,-1,-1,0,-1,-1).
%F A249019 a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3) + 5*a(n-4) + 6*a(n-5) - a(n-6) - a(n-7) - a(n-9) - a(n-10), for n>=16.
%F A249019 G.f.: (1 + 2*x + 4*x^2 + 9*x^3 + 22*x^4 + 60*x^5 - 8*x^6 - 14*x^7 - 8*x^9 - 26*x^10 + 3*x^12 + 3*x^15)/(1 - x - 2*x^2 - 3*x^3 - 5* x^4 - 6*x^5 + x^6 + x^7 + x^9 + x^10). - _Colin Barker_, Jan 12 2015
%t A249019 LinearRecurrence[{1,2,3,5,6,-1,-1,0,-1,-1},{1,3,9,27,81,243,540,1440,3804,9960,25908,67344,175884,458832,1196364,3119304},40] (* _Harvey P. Dale_, Feb 05 2019 *)
%o A249019 (PARI) Vec(-12*x^6*(20*x^9 +27*x^8 +9*x^7 +23*x^6 +28*x^5 -110*x^4 -138*x^3 -107*x^2 -75*x -45) / (x^10 +x^9 +x^7 +x^6 -6*x^5 -5*x^4 -3*x^3 -2*x^2 -x +1) + O(x^100)) \\ _Colin Barker_, Jan 12 2015
%Y A249019 Cf. A248959, A248960.
%K A249019 nonn,easy
%O A249019 0,2
%A A249019 _Andrew Woods_, Jan 12 2015