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%I #11 Jan 26 2018 08:50:20
%S 256,840,2028,4184,7834,13720,22866,36656,56925,86064,127140,184032,
%T 261584,365776,503914,684840,919163,1219512,1600812,2080584,2679270,
%U 3420584,4331890,5444608,6794649,8422880,10375620,12705168,15470364
%N Number of length n+3 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.
%H R. H. Hardin, <a href="/A258733/b258733.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5040)*n^7 + (7/720)*n^6 + (29/144)*n^5 + (305/144)*n^4 + (1027/45)*n^3 + (16267/180)*n^2 + (2425/21)*n + 24 for n>1.
%F Empirical g.f.: x*(256 - 1208*x + 2476*x^2 - 2856*x^3 + 2026*x^4 - 904*x^5 + 242*x^6 - 32*x^7 + x^8) / (1 - x)^8. - _Colin Barker_, Jan 26 2018
%e Some solutions for n=4:
%e ..3....0....0....2....3....1....1....1....1....0....0....0....3....2....0....0
%e ..0....3....0....2....2....0....3....1....1....0....0....2....2....1....1....2
%e ..0....3....2....2....2....1....2....2....1....0....0....2....2....2....1....3
%e ..1....3....2....0....2....1....2....3....2....2....1....2....2....3....1....3
%e ..2....1....0....1....3....1....2....3....0....2....1....3....2....3....0....3
%e ..2....1....0....1....0....2....2....3....0....0....1....0....0....0....2....1
%e ..2....3....2....3....1....2....0....1....1....0....3....2....3....3....3....2
%Y Row 3 of A258730.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 08 2015
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