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%I #6 Dec 31 2023 15:52:38
%S 7,63,511,4091,32739,261905,2095233,16761837,134094563,1072755573,
%T 8582037499,68656243311,549249492763,4393992312383,35151909460619,
%U 281215043377605,2249718488563135,17997733040855701,143981745385748627
%N Hilltop maps: number of n X 3 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..4 n X 3 array.
%C Column 3 of A218288.
%H R. H. Hardin, <a href="/A218283/b218283.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) +6*a(n-6) +12*a(n-7) +10*a(n-8) +48*a(n-9) +9*a(n-10) +9*a(n-11) +9*a(n-12) +9*a(n-13) +9*a(n-14) +5*a(n-15) +13*a(n-16) +11*a(n-17) -52*a(n-18) -64*a(n-19) -64*a(n-20) -64*a(n-21) -63*a(n-22) -59*a(n-23) -48*a(n-24) -38*a(n-25) +13*a(n-26) +41*a(n-27) +48*a(n-28) +48*a(n-29) +48*a(n-30) +46*a(n-31) +33*a(n-32) +15*a(n-33) +5*a(n-34) -5*a(n-35) -7*a(n-36) -7*a(n-37) -7*a(n-38) -7*a(n-39) -6*a(n-40) -2*a(n-41) +2*a(n-42) -a(n-44) -a(n-45) -a(n-46) -a(n-47) -a(n-48) -a(n-49).
%e Some solutions for n=3
%e ..0..0..1....0..1..0....1..1..1....1..0..0....0..1..0....0..1..1....0..1..1
%e ..0..1..0....0..1..1....0..0..1....0..1..0....0..1..1....1..1..0....0..1..1
%e ..0..0..0....1..0..0....1..0..1....0..0..0....0..1..1....1..0..0....0..0..0
%Y Cf. A218288.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 25 2012