A188517 - OEIS

%I #7 Mar 31 2012 12:36:12

%S 7,49,229,1016,4143,16438,63575,242843,918833,3457086,12955090,

%T 48421778,180653858,673156166,2506152176,9324771027,34680539851,

%U 128945324565,479330913137,1781567026168,6621013690288,24604558144729,91429145674242

%N Number of nX3 binary arrays without the pattern 1 1 0 diagonally, vertically or horizontally

%C Column 3 of A188523

%H R. H. Hardin, <a href="/A188517/b188517.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=7*a(n-1)-5*a(n-2)-54*a(n-3)+79*a(n-4)+173*a(n-5)-294*a(n-6)-313*a(n-7)+521*a(n-8)+357*a(n-9)-501*a(n-10)-255*a(n-11)+272*a(n-12)+106*a(n-13)-84*a(n-14)-23*a(n-15)+14*a(n-16)+2*a(n-17)-a(n-18).

%F Empirical: G.f. -x*(-7 +79*x^2 -36*x^3 -269*x^4 +199*x^5 +422*x^6 -446*x^7 -410*x^8 +468*x^9 +269*x^10 -264*x^11 -109*x^12 +84*x^13 +23*x^14 -14*x^15 -2*x^16 +x^17) / ( (x-1) *(x^2-3*x+1) *(x^2-x-1) *(x^3-2*x^2-x+1) *(x^4+x^3-3*x^2-3*x+1) *(1+x)^2 *(x^2+x-1)^2 ). - R. J. Mathar, Dec 21 2011

%e Some solutions for 4X3

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 02 2011