A185489 - OEIS

%I #9 Feb 27 2018 11:58:45

%S 0,24,36,160,380,1332,3616,11828,33764,107240,314028,980996,2915008,

%T 9013892,27021076,83023720,250222428,765753844,2315518240,7068457300,

%U 21417487492,65277991272,198042102732,603022088996,1830890468736

%N Number of (n+1) X 2 binary arrays with every 2 X 2 subblock sum equal to some horizontal or vertical neighbor 2 X 2 subblock sum.

%C Column 1 of A185497.

%H R. H. Hardin, <a href="/A185489/b185489.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 14*a(n-3) + 24*a(n-4) - 16*a(n-5) - 24*a(n-6) + 16*a(n-7) - 64*a(n-8).

%F Empirical g.f.: 4*x^2*(6 - 9*x - 5*x^2 + 32*x^3 - 90*x^4 + 60*x^5 - 96*x^6) / ((1 - 2*x)*(1 - x - 5*x^2 + 4*x^3 - 16*x^4 - 16*x^5 - 8*x^6 - 32*x^7)). - _Colin Barker_, Feb 27 2018

%e Some solutions for 4 X 2:

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

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

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

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

%Y Cf. A185497.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 29 2011