|
%I #11 Feb 19 2018 11:01:46
%S 1,2,6,23,99,452,2136,10313,50469,249062,1235466,6147803,30650439,
%T 152986472,764135196,3818284493,19084248009,95399716682,476934013326,
%U 2384476356383,11921800651179,59607259863692,298031069141856
%N Number of n X 1 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
%C Column 1 of A233113.
%H R. H. Hardin, <a href="/A233106/b233106.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-1) - 23*a(n-2) + 15*a(n-3).
%F Conjectures from _Colin Barker_, Feb 19 2018: (Start)
%F G.f.: x*(1 - 7*x + 11*x^2) / ((1 - x)*(1 - 3*x)*(1 - 5*x)).
%F a(n) = (75 + 10*3^n + 3*5^n) / 120.
%F (End)
%e Some solutions for n=7:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....1....0....0....1....0....1....1....1....0....1....1....0....1....0....1
%e ..2....2....0....1....5....1....5....2....1....1....5....5....1....0....1....2
%e ..1....4....1....5....1....5....2....0....1....5....1....5....2....4....2....5
%e ..5....0....1....1....1....4....0....3....5....5....1....1....1....2....1....5
%e ..1....2....2....0....2....5....3....5....1....2....1....0....5....4....3....2
%e ..5....2....0....1....5....4....1....2....0....5....5....0....2....2....3....5
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 04 2013
| 