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%I #8 Jul 24 2018 09:39:50
%S 7,63,511,4081,32641,261121,2088919,16710911,133683711,1069441121,
%T 8555300481,68440576001,547509985575,4379962908223,35038767479807,
%U 280302653750609,2242361342901505,17938411659180033,143503460703541239
%N Hilltop maps: number of n X 3 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..2 n X 3 array.
%C Column 3 of A218319.
%H R. H. Hardin, <a href="/A218314/b218314.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) + 7*a(n-2) + 7*a(n-3) + 7*a(n-4) + 7*a(n-5).
%F Empirical g.f.: 7*x*(1 + x + x^2)^2 / (1 - 7*x - 7*x^2 - 7*x^3 - 7*x^4 - 7*x^5). - _Colin Barker_, Jul 24 2018
%e Some solutions for n=3:
%e ..1..1..1....0..1..1....1..0..0....0..1..0....1..0..0....1..1..0....0..0..1
%e ..1..1..0....1..0..0....0..0..1....0..0..1....0..1..1....0..1..0....0..1..1
%e ..1..1..0....0..1..1....1..0..0....1..0..1....0..0..1....1..0..1....1..1..1
%Y Cf. A218319.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 25 2012
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