A305288 - OEIS

%I #4 May 29 2018 08:24:24

%S 0,1,1,1,7,1,2,23,23,2,3,86,55,86,3,5,313,279,279,313,5,8,1145,895,

%T 1763,895,1145,8,13,4184,3696,8431,8431,3696,4184,13,21,15293,13289,

%U 46983,41446,46983,13289,15293,21,34,55895,51734,246893,301533,301533,246893

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4 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.....23......86......313.......1145........4184........15293

%C ..1....23.....55.....279......895.......3696.......13289........51734

%C ..2....86....279....1763.....8431......46983......246893......1332201

%C ..3...313....895....8431....41446.....301533.....1847322.....12314089

%C ..5..1145...3696...46983...301533....2636906....21092843....175328455

%C ..8..4184..13289..246893..1847322...21092843...214220078...2256259549

%C .13.15293..51734.1332201.12314089..175328455..2256259549..29751215558

%C .21.55895.192418.7128691.80678010.1483162272.24509450800.412395328914

%H R. H. Hardin, <a href="/A305288/b305288.txt">Table of n, a(n) for n = 1..219</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-1) +a(n-2) +4*a(n-3) +4*a(n-4)

%F k=3: [order 15] for n>16

%F k=4: [order 36] for n>41

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303890.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 29 2018