cp's OEIS Frontend

A200788 Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases.

%I A200788 #13 Oct 15 2017 20:28:02
%S A200788 64,622,3136,11100,31395,75992,164004,324087,597190,1039654,1726660,
%T A200788 2756026,4252353,6371520,9305528,13287693,18598188,25569934,34594840,
%U A200788 46130392,60706591,78933240,101507580,129222275,162973746,203770854
%N A200788 Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases.
%C A200788 Row 4 of A200785.
%H A200788 R. H. Hardin, <a href="/A200788/b200788.txt">Table of n, a(n) for n = 1..138</a>
%F A200788 Empirical: a(n) = (349/720)*n^6 + (321/80)*n^5 + (1883/144)*n^4 + (1013/48)*n^3 + (3139/180)*n^2 + (413/60)*n + 1.
%F A200788 Conjectures from _Colin Barker_, Oct 15 2017: (Start)
%F A200788 G.f.: x*(64 + 174*x + 126*x^2 - 30*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A200788 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 A200788 (End)
%e A200788 Some solutions for n=3
%e A200788 ..2....3....3....2....3....2....1....1....3....3....1....1....2....3....2....1
%e A200788 ..3....2....1....3....0....0....3....0....0....3....3....1....2....3....2....1
%e A200788 ..0....3....3....3....0....1....3....0....1....0....3....3....1....0....2....1
%e A200788 ..3....3....2....3....3....1....0....2....1....2....0....0....0....2....2....2
%e A200788 ..3....1....2....3....0....1....1....1....3....0....2....0....3....2....1....2
%e A200788 ..3....3....1....2....0....2....1....2....3....0....2....2....1....2....2....3
%K A200788 nonn
%O A200788 1,1
%A A200788 _R. H. Hardin_, Nov 22 2011