%I #4 Jan 06 2017 11:31:59

%S 1,2,2,4,7,4,8,18,18,8,16,50,45,50,16,32,138,116,116,138,32,64,383,

%T 293,302,293,383,64,128,1063,735,726,726,735,1063,128,256,2951,1844,

%U 1709,1648,1709,1844,2951,256,512,8193,4626,3996,3647,3647,3996,4626,8193,512

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ...1.....2.....4.....8....16.....32.....64....128....256.....512....1024

%C ...2.....7....18....50...138....383...1063...2951...8193...22748...63161

%C ...4....18....45...116...293....735...1844...4626..11611...29151...73200

%C ...8....50...116...302...726...1709...3996...9346..21891...51367..120680

%C ..16...138...293...726..1648...3647...8031..17745..39427...87996..197061

%C ..32...383...735..1709..3647...7594..15792..33136..70293..150510..324417

%C ..64..1063..1844..3996..8031..15792..31152..62349.126893..261994..546766

%C .128..2951..4626..9346.17745..33136..62349.119656.234789..469715..953647

%C .256..8193.11611.21891.39427..70293.126893.234789.446500..869877.1726530

%C .512.22748.29151.51367.87996.150510.261994.469715.869877.1658080.3232058

%H R. H. Hardin, <a href="/A280604/b280604.txt">Table of n, a(n) for n = 1..510</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6)

%F k=3: a(n) = 4*a(n-1) -3*a(n-2) -3*a(n-3) +2*a(n-4) +3*a(n-5) -2*a(n-6) for n>8

%F k=4: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-5) -3*a(n-7) +2*a(n-8) +a(n-9) -a(n-10) for n>13

%F k=5: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-6) -2*a(n-7) -3*a(n-8) +5*a(n-9) -a(n-10) -a(n-11) -a(n-12) +a(n-13) for n>15

%F k=6: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-7) -2*a(n-8) -3*a(n-9) +5*a(n-10) -a(n-11) -a(n-12) -a(n-14) +a(n-15) for n>19

%F k=7: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-8) -2*a(n-9) -3*a(n-10) +5*a(n-11) -a(n-12) -a(n-13) -a(n-16) +a(n-17) for n>22

%e Some solutions for n=4 k=4

%e ..0..0..1..0. .0..1..0..0. .0..1..1..1. .0..1..0..0. .0..1..0..1

%e ..1..0..1..0. .1..0..1..0. .0..0..0..0. .1..0..1..0. .0..1..0..1

%e ..1..0..1..0. .0..1..0..1. .1..1..1..0. .1..1..0..1. .0..1..0..0

%e ..1..1..0..1. .0..0..1..0. .0..0..0..1. .0..0..1..1. .0..1..1..1

%Y Column 1 is A000079(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 06 2017