|
%I #8 Aug 21 2017 13:10:54
%S 15,2825,100236,1447334,12123567,70617807,317518832,1176570012,
%T 3753186183,10625460549,27293238764,64668634914,143140038743,
%U 298924843947,593647442496,1128342108536,2063388866271,3646247928129
%N Number of length 5+5 0..n arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms.
%C Row 5 of A249960.
%H R. H. Hardin, <a href="/A249965/b249965.txt">Table of n, a(n) for n = 1..147</a>
%F Empirical: a(n) = n^10 + (4/45)*n^9 + (31/6)*n^8 + (634/315)*n^7 - (21/20)*n^6 + (761/90)*n^5 - (19/12)*n^4 - (21/10)*n^3 + (119/30)*n^2 - (67/70)*n.
%F Conjectures from _Colin Barker_, Aug 21 2017: (Start)
%F G.f.: x*(15 + 2660*x + 69986*x^2 + 497638*x^3 + 1254698*x^4 + 1248320*x^5 + 488690*x^6 + 65078*x^7 + 1715*x^8) / (1 - x)^11.
%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
%F (End)
%e Some solutions for n=3:
%e ..3....3....3....1....1....1....3....2....0....2....1....2....1....0....1....0
%e ..2....0....2....2....2....1....3....2....3....0....0....1....1....1....3....0
%e ..2....3....3....0....3....2....0....0....1....0....3....2....0....3....2....3
%e ..0....1....1....2....0....0....3....2....0....2....2....2....3....2....0....2
%e ..0....3....3....2....0....0....0....3....2....1....0....1....3....3....3....2
%e ..2....3....1....0....2....2....3....1....2....2....1....3....0....3....3....3
%e ..3....0....3....3....3....3....3....0....2....3....3....3....1....3....1....0
%e ..3....0....3....1....3....1....2....2....2....0....3....0....2....1....3....0
%e ..3....2....3....0....3....2....1....0....1....3....3....0....2....3....3....3
%e ..3....2....1....1....3....0....2....2....0....0....0....2....0....0....0....1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 09 2014
| 