A302680 - OEIS

%I #4 Apr 11 2018 12:28:33

%S 1,2,2,3,3,4,5,3,4,8,8,5,8,6,16,13,7,12,7,9,32,21,13,18,20,11,14,64,

%T 34,23,40,30,33,18,22,128,55,37,94,76,63,64,29,35,256,89,63,184,217,

%U 187,125,121,47,56,512,144,109,358,509,661,453,257,231,76,90,1024,233,183,760

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1..2..3...5....8...13....21.....34......55.......89......144.......233

%C ...2..3..3...5....7...13....23.....37......63......109......183.......309

%C ...4..4..8..12...18...40....94....184.....358......760.....1594......3220

%C ...8..6..7..20...30...76...217....509....1189.....3034.....7569.....18274

%C ..16..9.11..33...63..187...661...1837....5075....15661....46975....135191

%C ..32.14.18..64..125..453..2013...6725...21745....80985...295335...1015113

%C ..64.22.29.121..257.1125..6311..25139...96728...439233..1942666...8017639

%C .128.35.47.231..528.2782.19497..92889..422915..2330640.12480973..61679118

%C .256.56.76.440.1085.6843.60253.343421.1847358.12346637.80210343.474618407

%H R. H. Hardin, <a href="/A302680/b302680.txt">Table of n, a(n) for n = 1..799</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) -a(n-3)

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

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

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

%F k=6: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +a(n-4) -2*a(n-5) -a(n-6) for n>12

%F k=7: [order 12] for n>19

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-2)

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

%F n=3: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) for n>7

%F n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +5*a(n-4) -3*a(n-5) -3*a(n-6) +2*a(n-7) for n>11

%F n=5: [order 11] for n>16

%F n=6: [order 17] for n>23

%F n=7: [order 31] for n>38

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A001611(n+1).

%Y Row 1 is A000045(n+1).

%Y Row 2 is A003229(n-1) for n>2.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 11 2018