A218200 - OEIS

%I #7 Mar 09 2018 19:33:57

%S 3,15,59,233,929,3697,14719,58599,233291,928769,3697573,14720617,

%T 58605079,233315983,928867415,3697966433,14722182653,58611311377,

%U 233340796147,928966198975,3698359708575,14723748344241,58617544637937

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

%C Column 2 of A218206.

%H R. H. Hardin, <a href="/A218200/b218200.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) + 2*a(n-4) + 2*a(n-5) - a(n-6) - a(n-7) - a(n-8) - a(n-9).

%F Empirical g.f.: x*(3 + 6*x + 5*x^2 + 2*x^3 + 2*x^4 - 2*x^5 - 3*x^6 - 2*x^7 - x^8) / (1 - 3*x - 3*x^2 - 3*x^3 - 2*x^4 - 2*x^5 + x^6 + x^7 + x^8 + x^9). - _Colin Barker_, Mar 09 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A218206.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 23 2012