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%I #8 Jan 26 2018 08:06:59
%S 64,225,608,1408,2936,5664,10280,17754,29416,47047,72984,110240,
%T 162640,234974,333168,464474,637680,863341,1154032,1524624,1992584,
%U 2578300,3305432,4201290,5297240,6629139,8237800,10169488,12476448,15217466
%N Number of length n+2 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.
%C Row 2 of A258730.
%H R. H. Hardin, <a href="/A258732/b258732.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (5/4)*n^4 + (5167/720)*n^3 + (2489/120)*n^2 + (2591/105)*n + 10.
%F Empirical g.f.: x*(64 - 287*x + 600*x^2 - 740*x^3 + 576*x^4 - 282*x^5 + 80*x^6 - 10*x^7) / (1 - x)^8. - _Colin Barker_, Jan 26 2018
%e Some solutions for n=4:
%e ..0....2....2....1....1....0....2....1....3....0....2....0....1....1....0....1
%e ..0....2....2....1....0....0....3....2....0....2....3....0....1....1....2....1
%e ..1....3....2....2....1....3....1....3....1....2....3....3....3....2....2....3
%e ..2....3....2....3....1....0....1....1....1....1....0....2....0....2....3....0
%e ..1....3....3....0....1....1....2....1....2....2....1....3....0....0....3....1
%e ..3....0....0....0....0....2....3....1....2....3....3....3....0....0....0....3
%Y Cf. A258730.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 08 2015
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