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%I #14 Oct 16 2017 12:22:14
%S 232,932,3704,14932,60112,241718,971416,3904290,15693816,63085186,
%T 253583656,1019321774,4097329180,16469898636,66203547550,266116375576,
%U 1069699742484,4299838717346,17283927781406,69475666835578
%N Number of 0..7 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
%C Column 7 of A200871.
%H R. H. Hardin, <a href="/A200870/b200870.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) +15*a(n-4) +6*a(n-5) +12*a(n-6) +16*a(n-7) +7*a(n-8) +5*a(n-9) +4*a(n-10) +a(n-11).
%F Empirical g.f.: 2*x*(116 + 2*x + 220*x^2 + 526*x^3 + 292*x^4 + 473*x^5 + 552*x^6 + 257*x^7 + 180*x^8 + 132*x^9 + 32*x^10) / (1 - 4*x + 2*x^2 - 4*x^3 - 15*x^4 - 6*x^5 - 12*x^6 - 16*x^7 - 7*x^8 - 5*x^9 - 4*x^10 - x^11). - _Colin Barker_, Oct 16 2017
%e Some solutions for n=3
%e ..7....7....7....2....2....2....4....1....6....1....6....0....6....5....7....5
%e ..5....1....5....6....4....2....6....5....2....1....6....0....5....3....3....4
%e ..5....1....5....6....7....4....6....5....0....1....4....1....4....3....2....4
%e ..3....4....4....3....7....7....4....5....0....2....0....1....4....3....1....4
%e ..3....6....0....1....1....7....0....6....7....2....0....3....6....0....1....2
%t a[0,x_,y_] := 1; a[n_,x_,y_] := a[n,x,y] = Sum[If[z <=x<= y || y <=x<= z, a[n-1, z, x], 0], {z, 8}]; a[n_] := Sum[a[n, x, y], {x, 8}, {y, 8}]; Array[a, 25] (* _Giovanni Resta_, Mar 05 2014 *)
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011
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