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%I #11 Jan 25 2018 02:52:18
%S 237,694,2040,5997,17622,51768,152106,446932,1313199,3858468,11337057,
%T 33310953,97875387,287580727,844979241,2482746381,7294888809,
%U 21434086890,62978352609,185045107303,543705739710,1597534436091,4693929248088
%N Number of length n+4 0..2 arrays with at most two downsteps in every 4 consecutive neighbor pairs.
%C Column 4 of A255622.
%H R. H. Hardin, <a href="/A255618/b255618.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -a(n-3) +3*a(n-4) -3*a(n-5) -8*a(n-6) +9*a(n-7) -3*a(n-8) +a(n-9).
%F Empirical g.f.: x*(237 - 17*x - 42*x^2 + 114*x^3 - 386*x^4 - 429*x^5 + 657*x^6 - 216*x^7 + 81*x^8) / ((1 - x)*(1 - 2*x - 2*x^2 - x^3 - 4*x^4 - x^5 + 7*x^6 - 2*x^7 + x^8)). - _Colin Barker_, Jan 24 2018
%e Some solutions for n=4:
%e 1 0 2 0 1 2 2 1 2 2 2 2 0 2 1 0
%e 0 0 1 1 2 1 1 1 2 0 0 0 2 2 0 0
%e 0 2 2 2 0 2 1 1 1 2 0 2 0 1 2 1
%e 1 1 1 2 2 0 2 2 0 2 1 2 0 2 0 2
%e 2 1 1 0 2 0 2 2 2 2 2 1 2 1 2 0
%e 2 2 1 0 1 0 0 1 2 0 2 1 2 1 0 2
%e 1 0 1 2 2 2 0 0 1 1 0 1 1 2 0 0
%e 2 1 0 0 0 1 0 0 2 2 2 0 2 2 1 0
%Y Cf. A255622.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 28 2015
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