A200889 - OEIS

%I #10 Oct 16 2017 12:23:14

%S 37,292,1268,3985,10213,22736,45648,84681,147565,244420,388180,595049,

%T 884989,1282240,1815872,2520369,3436245,4610692,6098260,7961569,

%U 10272053,13110736,16569040,20749625,25767261,31749732,38838772,47191033,56979085

%N Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors.

%C Row 4 of A200886.

%H R. H. Hardin, <a href="/A200889/b200889.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (2/45)*n^6 + (19/15)*n^5 + (217/36)*n^4 + (71/6)*n^3 + (2057/180)*n^2 + (27/5)*n + 1.

%F Conjectures from _Colin Barker_, Oct 16 2017: (Start)

%F G.f.: x*(37 + 33*x + x^2 - 54*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=3

%e ..1....0....3....0....2....2....1....0....1....3....2....3....2....2....3....2

%e ..0....1....1....3....1....3....1....0....1....0....2....3....3....1....1....2

%e ..1....2....0....3....3....3....2....0....0....1....1....0....3....0....3....2

%e ..3....2....1....0....3....2....2....1....1....2....0....0....1....0....3....2

%e ..3....2....2....0....1....2....3....2....2....2....1....2....0....2....2....1

%e ..3....3....2....3....1....0....3....2....2....1....2....2....3....3....2....0

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2011