A305516 - OEIS

%I #4 Jun 03 2018 13:20:59

%S 0,1,1,1,3,1,2,2,2,2,3,1,5,1,3,5,8,6,6,8,5,8,5,8,10,8,5,8,13,22,19,13,

%T 13,19,22,13,21,29,33,38,62,38,33,29,21,34,60,60,73,108,108,73,60,60,

%U 34,55,121,107,164,353,343,353,164,107,121,55,89,194,204,351,982,925,925,982

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 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.....21......34.......55........89

%C ..1..3...2...1....8....5....22.....29.....60.....121......194.......425

%C ..1..2...5...6....8...19....33.....60....107.....204......375.......677

%C ..2..1...6..10...13...38....73....164....351.....749.....1719......3710

%C ..3..8...8..13...62..108...353....982...2362....6902....17966.....48328

%C ..5..5..19..38..108..343...925...2627...7334...20665....56990....159501

%C ..8.22..33..73..353..925..3547..14118..43745..173690...619516...2147913

%C .13.29..60.164..982.2627.14118..61412.226004.1060302..4311525..17892039

%C .21.60.107.351.2362.7334.43745.226004.923608.4939048.23169076.107297290

%H R. H. Hardin, <a href="/A305516/b305516.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>6

%F k=3: [order 10] for n>13

%F k=4: [order 14] for n>17

%F k=5: [order 45] for n>49

%F k=6: [order 91] for n>100

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A297809 for n>2.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jun 03 2018