cp's OEIS Frontend

A268451 Number of length-n 0..2 arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

%I A268451 #8 Jan 13 2019 16:30:10
%S A268451 3,9,25,67,176,456,1169,2971,7496,18796,46880,116386,287775,709005,
%T A268451 1741247,4264131,10415559,25381773,61721980,149801330,362926749,
%U A268451 877831299,2120050410,5112962906,12314976142,29625637490,71188510125
%N A268451 Number of length-n 0..2 arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
%H A268451 R. H. Hardin, <a href="/A268451/b268451.txt">Table of n, a(n) for n = 1..210</a>
%F A268451 Empirical: a(n) = 6*a(n-1) - 13*a(n-2) + 14*a(n-3) - 10*a(n-4) + 4*a(n-5) - a(n-6).
%F A268451 Empirical g.f.: x*(3 - 9*x + 10*x^2 - 8*x^3 + 3*x^4 - x^5) / (1 - 3*x + 2*x^2 - x^3)^2. - _Colin Barker_, Jan 13 2019
%e A268451 Some solutions for n=9:
%e A268451 ..1....0....0....2....2....1....0....2....1....1....2....0....1....0....1....0
%e A268451 ..2....0....1....2....2....1....0....2....0....1....0....0....1....2....0....2
%e A268451 ..0....2....2....1....2....2....2....1....2....2....2....1....1....2....1....0
%e A268451 ..2....1....2....2....2....0....0....0....2....2....2....1....1....2....1....1
%e A268451 ..2....1....2....0....2....0....2....1....1....0....2....1....1....2....2....2
%e A268451 ..0....1....0....0....0....2....0....1....0....1....2....2....1....2....2....0
%e A268451 ..1....0....0....0....0....0....0....1....0....2....0....2....0....1....0....2
%e A268451 ..2....1....1....2....0....0....2....2....0....0....0....2....0....0....0....0
%e A268451 ..2....2....1....2....0....2....1....0....2....1....1....2....2....0....1....0
%Y A268451 Column 2 of A268457.
%K A268451 nonn
%O A268451 1,1
%A A268451 _R. H. Hardin_, Feb 04 2016