A208070 - OEIS

%I #8 Jun 27 2018 15:46:07

%S 12,144,216,1008,3696,12960,48840,179520,657000,2423280,8913456,

%T 32769360,120581784,443565696,1631571912,6002079552,22079078352,

%U 81218792016,298770650040,1099049754720,4042930839192,14872226620512,54708578740752

%N Number of 5 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

%C Row 5 of A208069.

%H R. H. Hardin, <a href="/A208070/b208070.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 4*a(n-2) + 19*a(n-3) + 10*a(n-4) + 5*a(n-5) - 27*a(n-6) - 2*a(n-7) - 4*a(n-8) + 8*a(n-9) for n>11.

%F Empirical g.f.: 12*x*(1 + 11*x + 2*x^2 - x^3 - 86*x^4 - 31*x^5 - 51*x^6 + 114*x^7 + 4*x^8 + 24*x^9 - 32*x^10) / ((1 - 2*x - 4*x^2 - 8*x^3)*(1 + x + 2*x^2 - 3*x^3 - x^5 + x^6)). - _Colin Barker_, Jun 27 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A208069.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2012