|
%I #4 Jul 03 2018 09:13:11
%S 0,1,1,1,7,1,2,16,16,2,3,45,57,45,3,5,120,182,182,120,5,8,333,712,946,
%T 712,333,8,13,928,2832,5256,5256,2832,928,13,21,2613,10696,26592,
%U 43568,26592,10696,2613,21,34,7400,41107,139705,325839,325839,139705,41107
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1......1.......2.........3..........5............8............13
%C ..1....7.....16......45.......120........333..........928..........2613
%C ..1...16.....57.....182.......712.......2832........10696.........41107
%C ..2...45....182.....946......5256......26592.......139705........743357
%C ..3..120....712....5256.....43568.....325839......2520180......19750414
%C ..5..333...2832...26592....325839....3624515.....39827783.....450251619
%C ..8..928..10696..139705...2520180...39827783....621643922...10080547097
%C .13.2613..41107..743357..19750414..450251619..10080547097..235652502418
%C .21.7400.157988.3895564.153125421.5054524591.161747868059.5454074957154
%H R. H. Hardin, <a href="/A316448/b316448.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 20] for n>21
%F k=4: [order 69] for n>71
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..0..0. .0..1..1..0. .0..1..1..0. .0..1..0..0
%e ..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..0..1..1. .1..1..0..1
%e ..1..0..0..1. .0..0..1..0. .0..0..1..1. .0..1..1..1. .0..0..0..0
%e ..1..1..1..1. .1..0..1..0. .1..1..1..1. .0..0..1..0. .1..0..0..1
%e ..0..0..0..0. .1..1..1..0. .1..0..1..0. .1..0..1..1. .0..0..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304013.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 03 2018
| 