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A242235 Number of length n+4+1 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+2 elements, and new values 0..4 introduced in order.

%I A242235 #20 Jan 05 2019 07:54:21
%S A242235 15,35,71,139,271,531,1047,2059,4047,7955,15639,30747,60447,118835,
%T A242235 233623,459291,902943,1775139,3489831,6860827,13488031,26516771,
%U A242235 52130599,102486059,201482287,396103747,778719463,1530922155,3009713711
%N A242235 Number of length n+4+1 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+2 elements, and new values 0..4 introduced in order.
%H A242235 R. H. Hardin, <a href="/A242235/b242235.txt">Table of n, a(n) for n = 1..210</a>
%F A242235 Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5).
%F A242235 Conjecture: a(n) = 16*A145113(n-1) + A004767(n-2), n > 1. - _R. J. Mathar_, Aug 16 2017
%F A242235 Empirical g.f.: x*(15 + 20*x + 21*x^2 + 18*x^3 + 11*x^4) / (1 - x - x^2 - x^3 - x^4 - x^5). - _Colin Barker_, Oct 31 2018
%e A242235 Some solutions for n=5:
%e A242235   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
%e A242235   0  1  1  1  1  1  1  1  1  0  1  1  0  1  1  1
%e A242235   1  2  2  2  2  0  2  0  0  1  2  2  1  2  2  2
%e A242235   2  3  0  1  3  2  3  2  2  2  2  3  2  0  3  0
%e A242235   3  2  3  3  4  3  0  3  3  3  3  4  3  3  0  3
%e A242235   4  4  4  4  1  4  4  4  4  4  4  1  4  4  4  4
%e A242235   1  0  1  0  0  1  1  0  0  2  0  0  0  0  1  2
%e A242235   0  1  2  3  2  2  2  1  1  0  1  2  1  1  2  1
%e A242235   4  3  3  2  2  0  3  1  3  1  2  4  2  2  3  0
%e A242235   2  0  0  1  3  1  4  2  2  0  1  3  2  2  0  1
%Y A242235 Cf. A004767, A145113, A242239.
%Y A242235 Column 4 of A242239.
%K A242235 nonn
%O A242235 1,1
%A A242235 _R. H. Hardin_, May 08 2014