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A240652 Number of nX4 0..1 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..1 introduced in row major order.

%I A240652 #6 Jul 23 2025 11:05:21
%S A240652 1,3,17,91,352,1545,7154,33269,154974,724237,3394852,15935126,
%T A240652 74854028,351802659,1653966146,7777530146,36577083726,172031838421,
%U A240652 809149353515,3805931188358,17901967673107,84206433807963,396088887787212
%N A240652 Number of nX4 0..1 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..1 introduced in row major order.
%C A240652 Column 4 of A240656
%H A240652 R. H. Hardin, <a href="/A240652/b240652.txt">Table of n, a(n) for n = 1..210</a>
%F A240652 Empirical: a(n) = 6*a(n-1) -5*a(n-2) +2*a(n-3) -17*a(n-4) -64*a(n-5) -92*a(n-6) +24*a(n-7) +159*a(n-8) +803*a(n-9) +1491*a(n-10) +1970*a(n-11) +1678*a(n-12) -661*a(n-13) -5546*a(n-14) -11953*a(n-15) -18840*a(n-16) -20162*a(n-17) -13954*a(n-18) +3124*a(n-19) +29982*a(n-20) +57408*a(n-21) +71870*a(n-22) +67778*a(n-23) +36825*a(n-24) -12790*a(n-25) -63687*a(n-26) -92941*a(n-27) -91422*a(n-28) -61244*a(n-29) -12245*a(n-30) +25219*a(n-31) +41068*a(n-32) +34422*a(n-33) +19986*a(n-34) +4392*a(n-35) -450*a(n-36) +906*a(n-37) +3453*a(n-38) +4580*a(n-39) +4351*a(n-40) +1645*a(n-41) -1495*a(n-42) -2735*a(n-43) -2047*a(n-44) -913*a(n-45) -160*a(n-46) +116*a(n-47) +114*a(n-48) +44*a(n-49) +8*a(n-50)
%e A240652 Some solutions for n=4
%e A240652 ..0..0..0..1....0..0..0..0....0..1..1..1....0..1..1..0....0..0..0..0
%e A240652 ..0..0..0..0....0..0..0..0....1..1..0..1....1..1..1..1....0..0..0..0
%e A240652 ..1..0..0..0....0..0..0..0....1..0..1..1....1..1..0..1....1..1..0..0
%e A240652 ..0..1..0..0....1..0..0..1....1..1..1..0....0..1..1..1....1..1..0..0
%K A240652 nonn
%O A240652 1,2
%A A240652 _R. H. Hardin_, Apr 09 2014