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A268781 T(n,k) = Number of n X k binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.

%I A268781 #6 May 24 2024 15:49:04
%S A268781 2,4,4,7,11,7,13,26,26,13,23,65,91,65,23,41,148,316,316,148,41,72,343,
%T A268781 1031,1462,1031,343,72,126,766,3354,6383,6383,3354,766,126,219,1709,
%U A268781 10615,27531,38483,27531,10615,1709,219,379,3752,33344,115391,224960
%N A268781 T(n,k) = Number of n X k binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.
%C A268781 Table starts
%C A268781 ...2....4......7......13........23.........41...........72...........126
%C A268781 ...4...11.....26......65.......148........343..........766..........1709
%C A268781 ...7...26.....91.....316......1031.......3354........10615.........33344
%C A268781 ..13...65....316....1462......6383......27531.......115391........478849
%C A268781 ..23..148...1031....6383.....38483.....224960......1288693.......7271509
%C A268781 ..41..343...3354...27531....224960....1755113.....13493468.....101738555
%C A268781 ..72..766..10615..115391...1288693...13493468....140404442....1425678976
%C A268781 .126.1709..33344..478849...7271509..101738555...1425678976...19400886875
%C A268781 .219.3752.103339.1957904..40511381..758303322..14341399141..262072220011
%C A268781 .379.8195.317958.7940136.223527424.5590121407.142487073304.3491534799847
%H A268781 R. H. Hardin, <a href="/A268781/b268781.txt">Table of n, a(n) for n = 1..1404</a>
%F A268781 Empirical for column k:
%F A268781 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4).
%F A268781 k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4).
%F A268781 k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6).
%F A268781 k=4: [order 8].
%F A268781 k=5: [order 12].
%F A268781 k=6: [order 16].
%F A268781 k=7: [order 28].
%e A268781 Some solutions for n=4, k=4
%e A268781 ..0..0..0..0. .1..0..0..1. .1..0..1..1. .0..1..0..1. .0..1..0..0
%e A268781 ..1..0..1..1. .0..0..1..0. .0..0..0..0. .1..0..0..0. .0..0..1..0
%e A268781 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A268781 ..0..0..0..0. .0..1..0..0. .1..0..1..0. .1..0..1..0. .0..1..0..1
%Y A268781 Column 1 is A208354(n+1).
%Y A268781 Diagonal is A143870.
%K A268781 nonn,tabl
%O A268781 1,1
%A A268781 _R. H. Hardin_, Feb 13 2016