cp's OEIS Frontend

A206857 Number of n X 2 0..2 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal.

%I A206857 #9 Feb 20 2018 14:37:41
%S A206857 9,81,625,4761,36481,279841,2146225,16459249,126225225,968018769,
%T A206857 7423717921,56932346025,436613028289,3348376640449,25678633973281,
%U A206857 196928934060769,1510244084935881,11582031898782801,88822372650180625
%N A206857 Number of n X 2 0..2 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal.
%C A206857 Column 2 of A206863.
%H A206857 R. H. Hardin, <a href="/A206857/b206857.txt">Table of n, a(n) for n = 1..210</a>
%F A206857 Empirical: a(n) = 8*a(n-1) -5*a(n-2) +18*a(n-3) +7*a(n-4) -2*a(n-5) -a(n-6).
%F A206857 Empirical g.f.: x*(9 + 9*x + 22*x^2 + 4*x^3 - 3*x^4 - x^5) / ((1 - x + 3*x^2 - x^3)*(1 - 7*x - 5*x^2 - x^3)). - _Colin Barker_, Feb 20 2018
%e A206857 Some solutions for n=4:
%e A206857 ..1..0....0..2....0..2....0..1....2..0....0..2....0..2....2..1....0..2....2..1
%e A206857 ..1..1....2..2....0..0....2..1....1..2....0..2....1..1....2..1....0..1....0..2
%e A206857 ..0..1....0..0....0..1....2..0....0..2....2..2....2..0....2..2....2..0....1..2
%e A206857 ..2..0....2..1....2..1....0..1....2..0....0..2....0..1....1..2....1..0....2..1
%Y A206857 Cf. A206863.
%K A206857 nonn
%O A206857 1,1
%A A206857 _R. H. Hardin_, Feb 13 2012