%I #4 May 07 2018 08:00:19
%S 1,2,2,3,5,3,5,7,7,5,8,17,9,17,8,13,31,19,19,31,13,21,49,33,44,33,49,
%T 21,34,103,53,80,80,53,103,34,55,193,89,140,176,140,89,193,55,89,327,
%U 155,244,320,320,244,155,327,89,144,641,261,436,582,651,582,436,261,641,144
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1...2...3...5....8...13....21....34....55.....89....144.....233.....377
%C ..2...5...7..17...31...49...103...193...327....641...1207....2129....4039
%C ..3...7...9..19...33...53....89...155...261....439....749....1271....2149
%C ..5..17..19..44...80..140...244...436...800...1444...2584....4630....8328
%C ..8..31..33..80..176..320...582..1112..2178...4222...8066...15568...30220
%C .13..49..53.140..320..651..1321..2673..5293..10668..21704...43407...86685
%C .21.103..89.244..582.1321..2945..6333.13315..28932..63006..134021..284831
%C .34.193.155.436.1112.2673..6333.14708.33148..76987.180185..411855..940653
%C .55.327.261.800.2178.5293.13315.33148.79188.192201.476031.1166023.2823979
%H R. H. Hardin, <a href="/A304133/b304133.txt">Table of n, a(n) for n = 1..511</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +4*a(n-3) -2*a(n-4) for n>5
%F k=3: a(n) = a(n-1) +2*a(n-3) for n>7
%F k=4: a(n) = a(n-1) +3*a(n-3) +a(n-5) -a(n-6) -5*a(n-7) -2*a(n-8) +2*a(n-10) for n>13
%F k=5: [order 16] for n>22
%F k=6: [order 45] for n>48
%F k=7: [order 79] for n>87
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..1. .0..1..1..1. .0..1..1..0. .0..0..1..1
%e ..0..0..0..1. .0..0..0..1. .0..0..1..1. .1..1..1..1. .0..0..0..1
%e ..0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..1
%e ..0..0..1..1. .0..0..0..0. .0..1..1..1. .1..1..1..0. .0..0..1..1
%e ..0..0..0..1. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A303677.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 07 2018