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A240519 T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order.

%I A240519 #6 Jul 23 2025 11:02:27
%S A240519 1,2,2,3,3,3,5,6,6,5,8,10,10,10,8,13,21,28,28,21,13,21,42,73,99,73,42,
%T A240519 21,34,86,196,326,326,196,86,34,55,179,515,1080,1376,1080,515,179,55,
%U A240519 89,370,1376,3765,6205,6205,3765,1376,370,89,144,770,3686,13282,28942,37624
%N A240519 T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order.
%C A240519 Table starts
%C A240519 ..1...2....3......5.......8.......13.........21..........34...........55
%C A240519 ..2...3....6.....10......21.......42.........86.........179..........370
%C A240519 ..3...6...10.....28......73......196........515........1376.........3686
%C A240519 ..5..10...28.....99.....326.....1080.......3765.......13282........46928
%C A240519 ..8..21...73....326....1376.....6205......28942......135093.......636475
%C A240519 .13..42..196...1080....6205....37624.....231665.....1440880......9082172
%C A240519 .21..86..515...3765...28942...231665....1906245....16000486....135790448
%C A240519 .34.179.1376..13282..135093..1440880...16000486...180760099...2056580724
%C A240519 .55.370.3686..46928..636475..9082172..135790448..2056580724..31517059634
%C A240519 .89.770.9914.166611.3024792.57688194.1158315893.23588995330.488025204070
%H A240519 R. H. Hardin, <a href="/A240519/b240519.txt">Table of n, a(n) for n = 1..220</a>
%F A240519 Empirical for column k:
%F A240519 k=1: a(n) = a(n-1) +a(n-2)
%F A240519 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A240519 k=3: [order 20]
%F A240519 k=4: [order 48]
%e A240519 Some solutions for n=4 k=4
%e A240519 ..0..0..0..1....0..1..1..1....0..1..0..1....0..0..1..0....0..1..0..1
%e A240519 ..1..0..1..1....0..0..1..0....1..1..1..0....1..1..1..1....1..0..0..0
%e A240519 ..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..0....0..1..0..1
%e A240519 ..1..0..1..0....1..0..1..0....1..0..0..0....1..0..1..1....1..1..1..0
%Y A240519 Column 1 is A000045(n+1)
%K A240519 nonn,tabl
%O A240519 1,2
%A A240519 _R. H. Hardin_, Apr 06 2014