A218236 - OEIS

%I #8 Mar 10 2018 04:53:10

%S 3,15,63,255,1017,4065,16257,65025,260091,1040319,4161087,16643583,

%T 66571281,266272929,1065042945,4259976705,17039126547,68153385231,

%U 272601057663,1090354299903,4361217485769,17444071124289,69773089368321

%N Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..3 n X 2 array.

%C Column 2 of A218242.

%H R. H. Hardin, <a href="/A218236/b218236.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 3*x*(1 + x)^2*(1 + x^2)^2 / (1 - 3*x - 3*x^2 - 3*x^3 - 3*x^4 - 3*x^5 - 3*x^6 - 3*x^7). - _Colin Barker_, Mar 10 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A218242.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 24 2012