A299839 - OEIS

%I #4 Feb 20 2018 08:15:50

%S 0,1,1,1,4,1,2,18,18,2,3,64,142,64,3,5,236,1000,1000,236,5,8,888,7388,

%T 13850,7388,888,8,13,3336,54611,198202,198202,54611,3336,13,21,12512,

%U 402928,2853873,5544044,2853873,402928,12512,21,34,46928,2973312

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1........1..........2.............3................5..................8

%C ..1.....4.......18.........64...........236..............888...............3336

%C ..1....18......142.......1000..........7388............54611.............402928

%C ..2....64.....1000......13850........198202..........2853873...........41026724

%C ..3...236.....7388.....198202.......5544044........156175241.........4390323230

%C ..5...888....54611....2853873.....156175241.......8606994457.......473261273932

%C ..8..3336...402928...41026724....4390323230.....473261273932.....50892107038125

%C .13.12512..2973312..589665345..123389988671...26017342950926...5471622342472717

%C .21.46928.21942164.8475712818.3468206088400.1430440832008036.588340577558059509

%H R. H. Hardin, <a href="/A299839/b299839.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) for n>4

%F k=3: [order 9] for n>10

%F k=4: [order 22] for n>23

%F k=5: [order 68] for n>69

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A231950(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Feb 20 2018