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A221449 Hilltop maps: number of 4Xn binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..1 4Xn array.

%I A221449 #6 Jul 23 2025 01:56:43
%S A221449 1,105,1473,18393,260557,3669101,51186449,715191073,9997750841,
%T A221449 139736151537,1953034926537,27297122633073,381525299372673,
%U A221449 5332483219348113,74530789226270781,1041698296419651789
%N A221449 Hilltop maps: number of 4Xn binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..1 4Xn array.
%C A221449 Row 4 of A221446
%H A221449 R. H. Hardin, <a href="/A221449/b221449.txt">Table of n, a(n) for n = 1..85</a>
%F A221449 Empirical: a(n) = 9*a(n-1) +33*a(n-2) +415*a(n-3) +1016*a(n-4) +4212*a(n-5) +4364*a(n-6) +6084*a(n-7) -16154*a(n-8) -52326*a(n-9) -58320*a(n-10) -23560*a(n-11) +258118*a(n-12) +206162*a(n-13) -324408*a(n-14) -244116*a(n-15) +148795*a(n-16) +166349*a(n-17) -20171*a(n-18) -24653*a(n-19) -40309*a(n-20) +12497*a(n-21) -8027*a(n-22) +28179*a(n-23) -16900*a(n-24) -1964*a(n-25) -8214*a(n-26) +1038*a(n-27) -2120*a(n-28) +2536*a(n-29) +134*a(n-30) +830*a(n-31) +228*a(n-32) +188*a(n-33) +16*a(n-34) +40*a(n-35) -a(n-36) +a(n-37) +a(n-38) -a(n-39)
%e A221449 Some solutions for n=3
%e A221449 ..1..1..0....1..1..1....1..1..0....0..1..1....1..0..0....0..1..1....0..1..0
%e A221449 ..1..1..1....0..1..0....1..0..1....0..1..0....0..1..0....1..1..0....0..0..0
%e A221449 ..1..0..1....0..0..0....0..1..0....1..0..1....0..1..0....0..0..0....1..1..1
%e A221449 ..1..1..1....1..1..1....0..0..1....1..1..0....0..0..1....1..1..0....0..1..0
%K A221449 nonn
%O A221449 1,2
%A A221449 _R. H. Hardin_ Jan 17 2013