A316686 - OEIS

%I #6 Nov 12 2022 19:38:32

%S 0,0,0,0,3,0,0,5,5,0,0,18,14,18,0,0,61,73,73,61,0,0,209,387,769,387,

%T 209,0,0,702,2000,6742,6742,2000,702,0,0,2381,10487,62314,101803,

%U 62314,10487,2381,0,0,8069,54957,570806,1591947,1591947,570806,54957,8069,0,0,27330

%N T(n,k) = Number of n X k 0..1 arrays with every element unequal to 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0....0......0........0..........0............0...............0

%C .0....3......5.......18.........61..........209.............702

%C .0....5.....14.......73........387.........2000...........10487

%C .0...18.....73......769.......6742........62314..........570806

%C .0...61....387.....6742.....101803......1591947........24891152

%C .0..209...2000....62314....1591947.....43037698......1155724711

%C .0..702..10487...570806...24891152...1155724711.....53245963290

%C .0.2381..54957..5242925..389069291..31086640568...2457712512055

%C .0.8069.287218.48153854.6084616648.836374058655.113464874364839

%H R. H. Hardin, <a href="/A316686/b316686.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 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) for n>6;

%F k=3: [order 15] for n>16;

%F k=4: [order 42] for n>44.

%e Some solutions for n=5, k=4

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

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

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

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

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

%Y Column 2 is A303684.

%Y Column 3 is A305017.

%Y Column 4 is A305018.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jul 10 2018