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A302163 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302163 #4 Apr 02 2018 14:49:25
%S A302163 1,2,2,3,3,4,5,9,6,8,8,17,7,10,16,13,25,12,17,21,32,21,65,20,29,31,42,
%T A302163 64,34,185,34,51,73,57,86,128,55,385,56,109,140,156,111,179,256,89,
%U A302163 649,94,206,296,280,361,265,370,512,144,1489,156,407,603,635,621,865,527,770
%N A302163 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302163 Table starts
%C A302163 ...1...2...3....5....8...13....21....34....55.....89....144.....233.....377
%C A302163 ...2...3...9...17...25...65...185...385...649...1489...3929....8609...15913
%C A302163 ...4...6...7...12...20...34....56....94...156....262....436.....730....1216
%C A302163 ...8..10..17...29...51..109...206...407...791...1584...3104....6165...12131
%C A302163 ..16..21..31...73..140..296...603..1288..2584...5456..11189...23561...48423
%C A302163 ..32..42..57..156..280..635..1247..2815..5524..12457..25230...55645..113410
%C A302163 ..64..86.111..361..621.1563..2853..7306.12963..33522..61775..157788..293072
%C A302163 .128.179.265..865.1451.3948..6870.19993.32005.100147.163475..531350..820788
%C A302163 .256.370.527.1970.3189.9405.15489.50691.75825.282597.409385.1667452.2263018
%H A302163 R. H. Hardin, <a href="/A302163/b302163.txt">Table of n, a(n) for n = 1..720</a>
%F A302163 Empirical for column k:
%F A302163 k=1: a(n) = 2*a(n-1)
%F A302163 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A302163 k=3: a(n) = a(n-1) +8*a(n-3) -6*a(n-4) -4*a(n-6) +4*a(n-7) for n>11
%F A302163 k=4: [order 15] for n>19
%F A302163 k=5: [order 12] for n>15
%F A302163 k=6: [order 15] for n>26
%F A302163 k=7: [order 27] for n>39
%F A302163 Empirical for row n:
%F A302163 n=1: a(n) = a(n-1) +a(n-2)
%F A302163 n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
%F A302163 n=3: a(n) = a(n-1) +a(n-2) -a(n-3) +2*a(n-4) for n>6
%F A302163 n=4: [order 22] for n>23
%F A302163 n=5: [order 36] for n>40
%F A302163 n=6: [order 35] for n>45
%F A302163 n=7: [order 80] for n>89
%e A302163 Some solutions for n=5 k=4
%e A302163 ..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..1..0
%e A302163 ..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .0..1..0..1
%e A302163 ..0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1
%e A302163 ..0..1..0..0. .0..1..0..1. .1..0..1..0. .0..1..1..0. .1..1..0..0
%e A302163 ..0..1..0..1. .1..0..0..1. .1..0..1..0. .1..0..1..0. .0..1..0..1
%Y A302163 Column 1 is A000079(n-1).
%Y A302163 Column 2 is A240513.
%Y A302163 Row 1 is A000045(n+1).
%K A302163 nonn,tabl
%O A302163 1,2
%A A302163 _R. H. Hardin_, Apr 02 2018