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A200888 Number of 0..n arrays x(0..4) of 5 elements without any interior element greater than both neighbors.

%I A200888 #10 Oct 16 2017 12:23:07
%S A200888 21,121,422,1121,2507,4977,9052,15393,24817,38313,57058,82433,116039,
%T A200888 159713,215544,285889,373389,480985,611934,769825,958595,1182545,
%U A200888 1446356,1755105,2114281,2529801,3008026,3555777,4180351,4889537,5691632,6595457
%N A200888 Number of 0..n arrays x(0..4) of 5 elements without any interior element greater than both neighbors.
%C A200888 Row 3 of A200886.
%H A200888 R. H. Hardin, <a href="/A200888/b200888.txt">Table of n, a(n) for n = 1..210</a>
%F A200888 Empirical: a(n) = (2/15)*n^5 + (11/6)*n^4 + (35/6)*n^3 + (23/3)*n^2 + (68/15)*n + 1.
%F A200888 Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F A200888 G.f.: x*(21 - 5*x + 11*x^2 - 16*x^3 + 6*x^4 - x^5) / (1 - x)^6.
%F A200888 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A200888 (End)
%e A200888 Some solutions for n=3
%e A200888 ..3....3....3....2....0....1....0....3....1....3....3....2....2....2....0....2
%e A200888 ..3....3....3....2....1....1....0....3....0....2....1....2....1....3....1....2
%e A200888 ..3....3....2....3....1....0....0....2....0....3....3....0....0....3....1....2
%e A200888 ..3....3....1....3....0....2....2....3....2....3....3....2....3....1....0....0
%e A200888 ..2....0....1....2....3....2....3....3....3....3....0....2....3....2....1....0
%K A200888 nonn
%O A200888 1,1
%A A200888 _R. H. Hardin_, Nov 23 2011