cp's OEIS Frontend

A200876 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors or less than both neighbors.

%I A200876 #10 Oct 16 2017 09:58:30
%S A200876 68,723,3882,14455,42744,107777,241718,495495,945790,1703537,2924076,
%T A200876 4819113,7670638,11846955,17820980,26190965,37703808,53281111,
%U A200876 74048150,101365923,136866444,182491453,240534714,313688075,405091466,518387013
%N A200876 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors or less than both neighbors.
%C A200876 Row 6 of A200871.
%H A200876 R. H. Hardin, <a href="/A200876/b200876.txt">Table of n, a(n) for n = 1..210</a>
%F A200876 Empirical: a(n) = (1/20160)*n^8 + (19/720)*n^7 + (211/288)*n^6 + (1889/360)*n^5 + (44167/2880)*n^4 + (15991/720)*n^3 + (5689/336)*n^2 + (391/60)*n + 1.
%F A200876 Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F A200876 G.f.: x*(68 + 111*x - 177*x^2 - 167*x^3 + 237*x^4 - 97*x^5 + 35*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F A200876 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 A200876 (End)
%e A200876 Some solutions for n=3
%e A200876 ..3....1....2....1....3....2....1....0....2....2....3....0....3....1....2....2
%e A200876 ..3....1....3....3....3....2....3....2....1....2....1....0....3....1....1....0
%e A200876 ..0....3....3....3....2....3....3....3....1....1....0....2....3....1....0....0
%e A200876 ..0....3....3....3....2....3....1....3....0....1....0....2....2....1....0....0
%e A200876 ..2....2....3....1....2....3....0....2....0....1....0....0....1....1....1....1
%e A200876 ..3....2....1....0....2....3....0....1....1....1....0....0....0....1....1....2
%e A200876 ..3....1....1....0....1....3....2....1....1....0....0....0....0....2....3....2
%e A200876 ..3....0....1....2....1....0....2....1....3....0....3....2....0....2....3....2
%K A200876 nonn
%O A200876 1,1
%A A200876 _R. H. Hardin_, Nov 23 2011