cp's OEIS Frontend

A200891 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors.

%I A200891 #10 Oct 16 2017 12:23:20
%S A200891 114,1691,11472,50995,173606,491533,1215616,2710413,5567530,10700151,
%T A200891 19461872,33793071,56398174,90957305,142375936,217076281,323334306,
%U A200891 471666355,675269520,950520011,1317533910,1800794821,2429853056
%N A200891 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors.
%C A200891 Row 6 of A200886.
%H A200891 R. H. Hardin, <a href="/A200891/b200891.txt">Table of n, a(n) for n = 1..210</a>
%F A200891 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 A200891 Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F A200891 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 A200891 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 A200891 (End)
%e A200891 Some solutions for n=3
%e A200891 ..3....2....2....0....0....3....3....1....1....3....1....3....2....0....0....3
%e A200891 ..1....3....0....3....1....0....0....1....3....3....3....3....1....0....0....0
%e A200891 ..1....3....3....3....3....0....0....0....3....3....3....1....2....1....3....1
%e A200891 ..3....3....3....3....3....3....0....3....0....0....3....0....2....1....3....1
%e A200891 ..3....2....3....3....2....3....1....3....1....0....3....0....2....1....0....2
%e A200891 ..0....0....0....2....0....1....1....2....3....1....2....1....0....3....2....2
%e A200891 ..2....0....1....0....1....0....1....1....3....1....1....1....1....3....2....2
%e A200891 ..2....2....1....2....1....0....3....3....2....2....2....3....3....2....2....1
%K A200891 nonn
%O A200891 1,1
%A A200891 _R. H. Hardin_, Nov 23 2011