A304697 - OEIS

%I #4 May 17 2018 09:55:35

%S 0,1,1,1,7,1,2,16,16,2,3,45,56,45,3,5,120,178,178,120,5,8,333,669,918,

%T 669,333,8,13,928,2615,4910,4910,2615,928,13,21,2613,9573,24408,37050,

%U 24408,9573,2613,21,34,7400,35581,124399,263381,263381,124399,35581,7400

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 6 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.....56.....178......669.......2615........9573.........35581

%C ..2...45....178.....918.....4910......24408......124399........641663

%C ..3..120....669....4910....37050.....263381.....1894297......13791026

%C ..5..333...2615...24408...263381....2753404....27769991.....285425506

%C ..8..928...9573..124399..1894297...27769991...389403912....5581948043

%C .13.2613..35581..641663.13791026..285425506..5581948043..111681916203

%C .21.7400.133149.3271834.99838011.2949991545.80739890302.2269676763262

%H R. H. Hardin, <a href="/A304697/b304697.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 19] for n>21

%F k=4: [order 69] for n>71

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304013.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 17 2018