cp's OEIS Frontend

A242318 Number of length n+3+2 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+3 elements, and new values 0..3 introduced in order.

%I A242318 #8 Nov 01 2018 06:43:10
%S A242318 65,185,503,1316,3398,8801,23069,60197,156887,408962,1066514,2781611,
%T A242318 7253453,18914369,49323167,128621684,335409314,874649537,2280834353,
%U A242318 5947765493,15510073823,40445831522,105471145814,275038567523
%N A242318 Number of length n+3+2 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+3 elements, and new values 0..3 introduced in order.
%H A242318 R. H. Hardin, <a href="/A242318/b242318.txt">Table of n, a(n) for n = 1..210</a>
%F A242318 Empirical: 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).
%F A242318 Empirical g.f.: x*(65 + 120*x + 188*x^2 + 248*x^3 + 196*x^4 - 53*x^5 - 36*x^6 - 16*x^7 - 49*x^8 - 35*x^9) / (1 - x - 2*x^2 - 3*x^3 - 5*x^4 - 6*x^5 + x^6 + x^7 + x^9 + x^10). - _Colin Barker_, Nov 01 2018
%e A242318 Some solutions for n=5:
%e A242318 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242318 ..0....0....1....1....0....1....0....1....1....0....1....1....1....1....1....1
%e A242318 ..0....1....0....2....1....1....1....2....1....1....2....2....2....1....2....2
%e A242318 ..1....2....1....0....2....2....2....3....2....2....3....0....0....2....3....3
%e A242318 ..2....3....2....3....0....3....3....1....3....3....2....3....1....1....0....1
%e A242318 ..3....0....3....3....3....0....2....2....0....1....0....2....3....3....1....1
%e A242318 ..1....1....0....1....2....1....0....0....1....0....3....2....2....0....3....0
%e A242318 ..3....1....2....2....1....2....3....2....0....2....1....1....0....1....1....2
%e A242318 ..0....2....1....0....3....1....1....3....2....3....0....2....2....2....2....0
%e A242318 ..3....0....1....0....2....3....1....0....2....0....0....0....3....3....3....3
%Y A242318 Column 3 of A242322.
%K A242318 nonn
%O A242318 1,1
%A A242318 _R. H. Hardin_, May 10 2014