A188559 - OEIS

%I #9 Apr 28 2018 07:43:49

%S 9,17,32,60,112,208,384,704,1280,2304,4097,7181,12381,20965,34831,

%T 56751,90683,142163,218790,330818,491870,719790,1037650,1474930,

%U 2068890,2866154,3924527,5315067,7124435,9457547,12440553,16224169,20987389

%N Number of 8 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.

%C Row 8 of A188553.

%H R. H. Hardin, <a href="/A188559/b188559.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (1/40320)*n^8 - (1/2016)*n^7 + (19/2880)*n^6 - (7/180)*n^5 + (1247/5760)*n^4 - (85/288)*n^3 + (17911/10080)*n^2 + (1961/840)*n + 5.

%F Conjectures from _Colin Barker_, Apr 28 2018: (Start)

%F G.f.: x*(9 - 64*x + 203*x^2 - 372*x^3 + 430*x^4 - 320*x^5 + 150*x^6 - 40*x^7 + 5*x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for 8 X 3:

%e ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1

%e ..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1

%e ..1..1..1....1..0..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1

%e ..1..1..1....0..0..0....1..1..1....1..1..1....1..1..1....1..1..0....1..1..1

%e ..1..1..1....0..0..0....1..1..1....1..1..1....1..1..1....1..0..0....1..1..0

%e ..1..1..0....0..0..0....1..1..1....1..0..0....1..1..1....0..0..0....1..0..0

%e ..0..0..0....0..0..0....1..1..1....0..0..0....1..1..0....0..0..0....0..0..0

%e ..0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..0..0

%Y Cf. A188553.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 04 2011