A300498 - OEIS

%I #4 Mar 07 2018 07:24:54

%S 1,2,2,4,7,4,8,18,18,8,16,50,52,50,16,32,138,143,143,138,32,64,383,

%T 412,499,412,383,64,128,1063,1225,1513,1513,1225,1063,128,256,2951,

%U 3699,4686,5837,4686,3699,2951,256,512,8193,11243,14822,19412,19412,14822,11243

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

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

%C ...4...18....52....143....412....1225.....3699.....11243.....34012.....102446

%C ...8...50...143....499...1513....4686....14822.....46717....149232.....478952

%C ..16..138...412...1513...5837...19412....66166....233796....816547....2856851

%C ..32..383..1225...4686..19412...77582...291721...1136238...4513729...17926620

%C ..64.1063..3699..14822..66166..291721..1296506...5589526..24694845..110652439

%C .128.2951.11243..46717.233796.1136238..5589526..28067098.138863892..695711878

%C .256.8193.34012.149232.816547.4513729.24694845.138863892.789286221.4445350963

%H R. H. Hardin, <a href="/A300498/b300498.txt">Table of n, a(n) for n = 1..220</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: [order 24] for n>25

%F k=4: [order 83] for n>86

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A280598.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 07 2018