A200891 - OEIS

%I #10 Oct 16 2017 12:23:20

%S 114,1691,11472,50995,173606,491533,1215616,2710413,5567530,10700151,

%T 19461872,33793071,56398174,90957305,142375936,217076281,323334306,

%U 471666355,675269520,950520011,1317533910,1800794821,2429853056

%N Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors.

%C Row 6 of A200886.

%H R. H. Hardin, <a href="/A200891/b200891.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/315)*n^8 + (134/315)*n^7 + (21/5)*n^6 + (571/36)*n^5 + (1841/60)*n^4 + (6047/180)*n^3 + (26603/1260)*n^2 + (299/42)*n + 1.

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

%F G.f.: x*(114 + 665*x + 357*x^2 - 953*x^3 - 37*x^4 - 47*x^5 + 37*x^6 - 9*x^7 + x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=3

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2011