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%I #7 Jan 26 2018 08:36:20
%S 65536,163020,220854,281136,370510,526672,752180,1038256,1394568,
%T 1831920,2362442,2999800,3759427,4658776,5717596,6958232,8405950,
%U 10089288,12040434,14295632,16895617,19886080,23318164,27248992,31742228,36868672
%N Number of length n+7 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.
%C Row 7 of A258730.
%H R. H. Hardin, <a href="/A258737/b258737.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5040)*n^7 + (11/720)*n^6 + (361/720)*n^5 + (1285/144)*n^4 + (40822/45)*n^3 + (1121411/180)*n^2 + (480457/35)*n + 7848 for n>5.
%F Empirical g.f.: x*(65536 - 361268*x + 751702*x^2 - 591152*x^3 - 236266*x^4 + 807960*x^5 - 664864*x^6 + 371040*x^7 - 206700*x^8 + 10940*x^9 + 117664*x^10 - 82072*x^11 + 17481*x^12) / (1 - x)^8. - _Colin Barker_, Jan 26 2018
%e Some solutions for n=2:
%e ..0....0....1....0....1....1....0....0....1....0....1....0....1....1....1....2
%e ..3....1....0....1....0....2....0....1....0....3....0....2....1....2....3....0
%e ..3....0....1....2....0....1....2....1....2....1....2....0....2....0....1....0
%e ..1....0....1....1....1....3....3....0....1....3....0....3....2....3....1....3
%e ..1....0....3....2....0....0....0....3....3....1....0....2....0....3....0....1
%e ..1....1....3....0....3....1....0....3....2....1....0....3....0....3....0....3
%e ..3....1....1....0....3....2....2....2....3....1....2....0....0....3....3....1
%e ..3....2....1....0....0....0....2....3....3....1....3....3....1....1....0....2
%e ..1....0....2....0....3....3....1....3....3....3....3....3....1....3....1....3
%Y Cf. A258730.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 08 2015
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