A299942 - OEIS

%I #4 Feb 22 2018 07:27:32

%S 1,2,2,4,8,4,8,25,25,8,16,85,70,85,16,32,286,205,205,286,32,64,969,

%T 614,649,614,969,64,128,3281,1860,2153,2153,1860,3281,128,256,11114,

%U 5631,7016,8379,7016,5631,11114,256,512,37649,17034,22819,30204,30204,22819

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 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........256

%C ...2.....8....25.....85.....286.....969.....3281.....11114......37649

%C ...4....25....70....205.....614....1860.....5631.....17034......51507

%C ...8....85...205....649....2153....7016....22819.....73931.....239461

%C ..16...286...614...2153....8379...30204...106323....379361....1353507

%C ..32...969..1860...7016...30204..124748...495413...2007099....8185319

%C ..64..3281..5631..22819..106323..495413..2237911..10459697...49578223

%C .128.11114.17034..73931..379361.2007099.10459697..57942564..326734318

%C .256.37649.51507.239461.1353507.8185319.49578223.326734318.2226744922

%H R. H. Hardin, <a href="/A299942/b299942.txt">Table of n, a(n) for n = 1..263</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) +2*a(n-3) -2*a(n-4) -4*a(n-5)

%F k=3: [order 11] for n>12

%F k=4: [order 22] for n>28

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A281338.

%Y Column 3 is A298282.

%Y Column 4 is A299176.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 22 2018