%I #7 Feb 19 2018 09:07:36
%S 1,3,7,15,29,57,113,225,449,895,1783,3551,7073,14089,28065,55905,
%T 111361,221827,441871,880191,1753309,3492529,6956993,13858081,
%U 27604801,54987775,109533679,218187167,434621025,865749521,1724542049,3435226017
%N Hilltop maps: number of n X 1 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..3 n X 1 array.
%C Column 1 of A218196.
%H R. H. Hardin, <a href="/A218189/b218189.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7).
%F Empirical g.f.: x*(1 + x)^2*(1 + x^2)^2 / (1 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7). - _Colin Barker_, Feb 19 2018
%e All solutions for n=3:
%e ..1....1....1....0....0....0....1
%e ..0....1....0....1....0....1....1
%e ..1....0....0....1....1....0....1
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 23 2012