A242318 - OEIS

%I #8 Nov 01 2018 06:43:10

%S 65,185,503,1316,3398,8801,23069,60197,156887,408962,1066514,2781611,

%T 7253453,18914369,49323167,128621684,335409314,874649537,2280834353,

%U 5947765493,15510073823,40445831522,105471145814,275038567523

%N 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 R. H. Hardin, <a href="/A242318/b242318.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=5:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....1....1....0....1....0....1....1....0....1....1....1....1....1....1

%e ..0....1....0....2....1....1....1....2....1....1....2....2....2....1....2....2

%e ..1....2....1....0....2....2....2....3....2....2....3....0....0....2....3....3

%e ..2....3....2....3....0....3....3....1....3....3....2....3....1....1....0....1

%e ..3....0....3....3....3....0....2....2....0....1....0....2....3....3....1....1

%e ..1....1....0....1....2....1....0....0....1....0....3....2....2....0....3....0

%e ..3....1....2....2....1....2....3....2....0....2....1....1....0....1....1....2

%e ..0....2....1....0....3....1....1....3....2....3....0....2....2....2....2....0

%e ..3....0....1....0....2....3....1....0....2....0....0....0....3....3....3....3

%Y Column 3 of A242322.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 10 2014