A317043 - OEIS

%I #4 Jul 19 2018 19:41:24

%S 1,2,2,3,5,3,5,9,9,5,8,21,14,21,8,13,57,33,33,57,13,21,125,90,141,90,

%T 125,21,34,289,204,610,610,204,289,34,55,741,527,2516,6188,2516,527,

%U 741,55,89,1737,1547,14294,35318,35318,14294,1547,1737,89,144,4045,4509,88030

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

%C Table starts

%C ..1....2....3......5........8.........13...........21.............34

%C ..2....5....9.....21.......57........125..........289............741

%C ..3....9...14.....33.......90........204..........527...........1547

%C ..5...21...33....141......610.......2516........14294..........88030

%C ..8...57...90....610.....6188......35318.......333207........4194626

%C .13..125..204...2516....35318.....393048......7760044......159647483

%C .21..289..527..14294...333207....7760044....302924053....11244564485

%C .34..741.1547..88030..4194626..159647483..11244564485...789775871803

%C .55.1737.4509.509381.41147020.2883656719.374107033198.46866337730606

%H R. H. Hardin, <a href="/A317043/b317043.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) -a(n-2) +8*a(n-3) -8*a(n-4)

%F k=3: [order 17] for n>19

%F k=4: [order 52] for n>55

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304349.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 19 2018