|
%I #4 Jun 01 2018 11:11:19
%S 0,0,0,0,3,0,0,5,5,0,0,18,14,18,0,0,61,69,69,61,0,0,209,376,661,376,
%T 209,0,0,702,1891,5580,5580,1891,702,0,0,2381,9889,48148,79810,48148,
%U 9889,2381,0,0,8069,51283,418382,1117343,1117343,418382,51283,8069,0,0,27330
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0....0......0........0..........0............0..............0................0
%C .0....3......5.......18.........61..........209............702.............2381
%C .0....5.....14.......69........376.........1891...........9889............51283
%C .0...18.....69......661.......5580........48148.........418382..........3621421
%C .0...61....376.....5580......79810......1117343.......16062787........228184784
%C .0..209...1891....48148....1117343.....25891309......612656116......14339915102
%C .0..702...9889...418382...16062787....612656116....23996865179.....926180069711
%C .0.2381..51283..3621421..228184784..14339915102...926180069711...58862515324951
%C .0.8069.265582.31403562.3255027240.337239061289.35989846262523.3770741435617783
%H R. H. Hardin, <a href="/A305457/b305457.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 14] for n>16
%F k=4: [order 42] for n>43
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..0..0..1. .0..0..1..1. .0..0..1..0. .0..1..0..1
%e ..1..1..1..0. .1..1..0..1. .1..1..0..0. .1..1..1..1. .1..0..1..0
%e ..0..0..0..1. .1..0..1..1. .0..1..0..0. .0..0..0..1. .0..1..1..0
%e ..1..0..0..0. .0..0..0..1. .1..1..1..1. .1..1..0..0. .1..0..0..1
%e ..0..1..0..1. .1..1..0..1. .0..0..0..0. .0..1..1..1. .0..1..0..1
%Y Column 2 is A303684.
%Y Column 3 is A304060.
%Y Column 4 is A304061.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jun 01 2018
|
