A317429 - OEIS

%I #4 Jul 27 2018 22:04:11

%S 1,2,2,3,5,3,5,9,9,5,8,21,14,21,8,13,53,32,32,53,13,21,105,75,97,75,

%T 105,21,34,237,148,279,279,148,237,34,55,577,311,640,1097,640,311,577,

%U 55,89,1205,687,1666,2891,2891,1666,687,1205,89,144,2681,1443,4365,8887,9116

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

%C Table starts

%C ..1....2....3.....5.....8.....13......21.......34.......55........89........144

%C ..2....5....9....21....53....105.....237......577.....1205......2681.......6349

%C ..3....9...14....32....75....148.....311......687.....1443......3042.......6534

%C ..5...21...32....97...279....640....1666.....4365....11025.....28226......72631

%C ..8...53...75...279..1097...2891....8887....30029....89848....274792.....882160

%C .13..105..148...640..2891...9116...32359...125832...439409...1569243....5838001

%C .21..237..311..1666..8887..32359..135880...617692..2534229..10679366...46580215

%C .34..577..687..4365.30029.125832..617692..3452903.16763615..83384489..439271584

%C .55.1205.1443.11025.89848.439409.2534229.16763615.95798175.562775876.3505340437

%H R. H. Hardin, <a href="/A317429/b317429.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

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

%F k=3: [order 12]

%F k=4: [order 40] for n>41

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+1).

%Y Column 2 is A303963.

%Y Column 3 is A316422.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 27 2018