A296963 - OEIS

%I #4 Dec 22 2017 11:40:40

%S 1,1,1,1,6,1,1,16,16,1,1,31,60,31,1,1,96,177,177,96,1,1,301,869,910,

%T 869,301,1,1,801,3994,6506,6506,3994,801,1,1,2261,16348,44519,88469,

%U 44519,16348,2261,1,1,6746,71669,289576,1064451,1064451,289576,71669,6746,1,1

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 3 or 5 king-move neighboring 1s.

%C Table starts

%C .1....1......1........1..........1............1..............1...............1

%C .1....6.....16.......31.........96..........301............801............2261

%C .1...16.....60......177........869.........3994..........16348...........71669

%C .1...31....177......910.......6506........44519.........289576.........1933227

%C .1...96....869.....6506......88469......1064451.......11592086.......134880572

%C .1..301...3994....44519....1064451.....21225209......374855869......7251402774

%C .1..801..16348...289576...11592086....374855869....10777843410....340260590831

%C .1.2261..71669..1933227..134880572...7251402774...340260590831..17890820040132

%C .1.6746.320252.12967823.1582121415.141096153092.10761797803245.941238613911895

%H R. H. Hardin, <a href="/A296963/b296963.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) = 4*a(n-1) -5*a(n-2) +11*a(n-3) -18*a(n-4) +4*a(n-5)

%F k=3: [order 21]

%F k=4: [order 51]

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 22 2017