cp's OEIS Frontend

A200791 Number of 0..n arrays x(0..8) of 9 elements without any two consecutive increases.

%I A200791 #10 Oct 15 2017 20:28:31
%S A200791 512,14849,163020,1062500,4975322,18514405,58154912,160338680,
%T A200791 398601390,910893148,1941103528,3899741885,7449762880,13624665670,
%U A200791 23987233104,40838614531,67488892468,108601809395,170627966340,262342539690
%N A200791 Number of 0..n arrays x(0..8) of 9 elements without any two consecutive increases.
%C A200791 Row 7 of A200785.
%H A200791 R. H. Hardin, <a href="/A200791/b200791.txt">Table of n, a(n) for n = 1..135</a>
%F A200791 Empirical: a(n) = (99377/362880)*n^9 + (48247/13440)*n^8 + (243673/12096)*n^7 + (60529/960)*n^6 + (2076437/17280)*n^5 + (274529/1920)*n^4 + (952027/9072)*n^3 + (152461/3360)*n^2 + (26399/2520)*n + 1.
%F A200791 Conjectures from _Colin Barker_, Oct 15 2017: (Start)
%F A200791 G.f.: x*(512 + 9729*x + 37570*x^2 + 39065*x^3 + 11862*x^4 + 551*x^5 + 124*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.
%F A200791 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
%F A200791 (End)
%e A200791 Some solutions for n=3
%e A200791 ..0....0....0....0....0....1....1....1....3....0....1....0....1....1....3....1
%e A200791 ..0....0....0....3....3....3....3....3....0....3....3....3....0....1....1....3
%e A200791 ..3....0....2....0....1....0....0....1....0....2....3....3....2....2....0....1
%e A200791 ..2....1....0....3....0....3....0....3....1....2....1....3....1....2....1....0
%e A200791 ..2....1....3....3....0....0....2....3....0....3....1....1....0....3....1....0
%e A200791 ..3....3....2....0....3....0....0....1....2....3....3....0....3....2....3....2
%e A200791 ..2....2....2....3....2....2....0....1....1....1....2....1....1....0....1....1
%e A200791 ..1....3....3....2....3....0....0....3....1....0....2....1....0....1....0....0
%e A200791 ..3....0....1....2....3....1....3....2....3....2....2....0....0....0....3....2
%K A200791 nonn
%O A200791 1,1
%A A200791 _R. H. Hardin_, Nov 22 2011