A305245 - OEIS

%I #4 May 28 2018 08:43:22

%S 1,2,2,4,4,4,8,12,12,8,16,24,18,24,16,32,64,32,32,64,32,64,184,86,94,

%T 86,184,64,128,432,158,273,273,158,432,128,256,1088,343,767,1134,767,

%U 343,1088,256,512,2944,721,2128,3288,3288,2128,721,2944,512,1024,7360,1520

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ...2....4...12....24.....64.....184.....432.....1088......2944.......7360

%C ...4...12...18....32.....86.....158.....343......721......1520.......3228

%C ...8...24...32....94....273.....767....2128.....6150.....17387......49477

%C ..16...64...86...273...1134....3288...11731....39986....136448.....468584

%C ..32..184..158...767...3288...12521...55039...238455...1028982....4474894

%C ..64..432..343..2128..11731...55039..311014..1742187...9652212...54215925

%C .128.1088..721..6150..39986..238455.1742187.12726939..91021791..667854447

%C .256.2944.1520.17387.136448.1028982.9652212.91021791.841464188.8000379451

%H R. H. Hardin, <a href="/A305245/b305245.txt">Table of n, a(n) for n = 1..337</a>

%F Empirical for column k:

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

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

%F k=3: [order 8] for n>11

%F k=4: [order 28] for n>32

%F k=5: [order 34] for n>42

%F k=6: [order 98] for n>104

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303794.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 28 2018