login
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
7

%I #4 Mar 01 2018 07:58:07

%S 1,2,2,4,8,4,8,26,26,8,16,88,95,88,16,32,298,375,375,298,32,64,1012,

%T 1526,2030,1526,1012,64,128,3440,6198,12324,12324,6198,3440,128,256,

%U 11700,25034,71529,138215,71529,25034,11700,256,512,39804,101312,412094

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6, 7 or 8 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.....95......375.......1526........6198.........25034..........101312

%C ...8....88....375.....2030......12324.......71529........412094.........2398145

%C ..16...298...1526....12324.....138215.....1333242......12622937.......125646087

%C ..32..1012...6198....71529....1333242....20341795.....298472434......4660242199

%C ..64..3440..25034...412094...12622937...298472434....6717267728....162737578821

%C .128.11700.101312..2398145..125646087..4660242199..162737578821...6293324571337

%C .256.39804.410252.13965762.1244747820.72718129316.3942079842968.243019177909127

%H R. H. Hardin, <a href="/A300267/b300267.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 64] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A298189.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 01 2018