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A283543 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors.

%I A283543 #4 Mar 10 2017 09:31:11
%S A283543 2,4,4,7,11,8,13,27,33,16,24,76,127,98,32,44,201,578,573,291,64,81,
%T A283543 537,2369,4089,2615,865,128,149,1444,10069,25532,29558,11903,2570,256,
%U A283543 274,3859,42664,167920,282773,212441,54211,7637,512,504,10339,179733,1094959
%N A283543 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors.
%C A283543 Table starts
%C A283543 ....2.....4.......7........13..........24............44..............81
%C A283543 ....4....11......27........76.........201...........537............1444
%C A283543 ....8....33.....127.......578........2369.........10069...........42664
%C A283543 ...16....98.....573......4089.......25532........167920.........1094959
%C A283543 ...32...291....2615.....29558......282773.......2905717........29377334
%C A283543 ...64...865...11903....212441.....3109801......49760703.......778500603
%C A283543 ..128..2570...54211...1529463....34266804.....854841910.....20707472573
%C A283543 ..256..7637..246869..11006233...377393657...14672363665....550220030803
%C A283543 ..512.22693.1124239..79212552..4156954825..251901309671..14624495679716
%C A283543 .1024.67432.5119755.570077446.45786939720.4324419947902.388675661283840
%H A283543 R. H. Hardin, <a href="/A283543/b283543.txt">Table of n, a(n) for n = 1..313</a>
%F A283543 Empirical for column k:
%F A283543 k=1: a(n) = 2*a(n-1)
%F A283543 k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)
%F A283543 k=3: a(n) = 5*a(n-1) -a(n-2) -7*a(n-3) +10*a(n-4) +4*a(n-5) -8*a(n-6)
%F A283543 k=4: [order 8]
%F A283543 k=5: [order 21]
%F A283543 k=6: [order 27]
%F A283543 k=7: [order 59]
%F A283543 Empirical for row n:
%F A283543 n=1: a(n) = a(n-1) +a(n-2) +a(n-3)
%F A283543 n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3)
%F A283543 n=3: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) -6*a(n-4) +11*a(n-5) -2*a(n-6)
%F A283543 n=4: [order 8]
%F A283543 n=5: [order 21]
%F A283543 n=6: [order 32]
%F A283543 n=7: [order 69]
%e A283543 Some solutions for n=4 k=4
%e A283543 ..1..1..0..0. .0..1..0..0. .1..0..0..0. .0..0..1..0. .0..1..0..0
%e A283543 ..0..0..0..1. .0..0..1..0. .1..0..0..1. .1..0..0..1. .0..1..0..0
%e A283543 ..0..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..1. .1..0..0..1
%e A283543 ..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0. .1..0..0..1
%Y A283543 Column 1 is A000079.
%Y A283543 Column 2 is A282990.
%Y A283543 Row 1 is A000073(n+3).
%Y A283543 Row 2 is A282641.
%K A283543 nonn,tabl
%O A283543 1,1
%A A283543 _R. H. Hardin_, Mar 10 2017