A301491 - OEIS

%I #6 Apr 17 2022 22:28:54

%S 1,2,2,4,7,4,8,18,18,8,16,50,52,50,16,32,138,148,148,138,32,64,383,

%T 441,599,441,383,64,128,1063,1372,2354,2354,1372,1063,128,256,2951,

%U 4326,9415,15124,9415,4326,2951,256,512,8193,13641,38558,93753,93753,38558,13641

%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

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

%C ...4...18....52....148......441......1372........4326........13641

%C ...8...50...148....599.....2354......9415.......38558.......158994

%C ..16..138...441...2354....15124.....93753......594953......3838256

%C ..32..383..1372...9415....93753....903707.....8479276.....81180752

%C ..64.1063..4326..38558...594953...8479276...116648010...1642511178

%C .128.2951.13641.158994..3838256..81180752..1642511178..34593556316

%C .256.8193.42741.657238.24838061.782053062.23269383762.732289348979

%H R. H. Hardin, <a href="/A301491/b301491.txt">Table of n, a(n) for n = 1..199</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 89] for n>91.

%e Some solutions for n=5, k=4

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

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

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

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

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

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

%Y Column 2 is A280598.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 22 2018