A207109 - OEIS

%I #9 Jun 19 2018 03:32:51

%S 18,324,1504,4534,10898,22714,42874,75198,124602,197280,300900,444814,

%T 640282,900710,1241902,1682326,2243394,2949756,3829608,4915014,

%U 6242242,7852114,9790370,12108046,14861866,18114648,21935724,26401374,31595274

%N Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%C Column 6 of A207111.

%H R. H. Hardin, <a href="/A207109/b207109.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (7/360)*n^6 + (77/120)*n^5 + (635/72)*n^4 + (623/24)*n^3 - (511/180)*n^2 - (103/5)*n + 6.

%F Conjectures from _Colin Barker_, Jun 19 2018: (Start)

%F G.f.: 2*x*(9 + 99*x - 193*x^2 + 90*x^3 + 17*x^4 - 18*x^5 + 3*x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207111.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2012