login
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.
7

%I #4 Jan 31 2018 09:27:27

%S 1,2,2,4,8,4,8,26,26,8,16,88,94,88,16,32,298,372,372,298,32,64,1012,

%T 1510,1977,1510,1012,64,128,3440,6105,11553,11553,6105,3440,128,256,

%U 11700,24546,63472,111695,63472,24546,11700,256,512,39804,98995,350339,881525

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ...2.....8.....26.......88.......298........1012.........3440..........11700

%C ...4....26.....94......372......1510........6105........24546..........98995

%C ...8....88....372.....1977.....11553.......63472.......350339........1960512

%C ..16...298...1510....11553....111695......881525......7133441.......61902351

%C ..32..1012...6105....63472....881525.....9369586....103514554.....1240234582

%C ..64..3440..24546...350339...7133441...103514554...1591404390....26808046076

%C .128.11700..98995..1960512..61902351..1240234582..26808046076...667156890263

%C .256.39804.399424.10931666.518059406.14225843633.428444704211.15251414560006

%H R. H. Hardin, <a href="/A299008/b299008.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 18] for n>19

%F k=4: [order 65] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A298189.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 31 2018