A316518 - OEIS

%I #4 Jul 05 2018 07:17:07

%S 1,2,2,4,8,4,8,21,21,8,16,49,28,49,16,32,120,75,75,120,32,64,293,174,

%T 204,174,293,64,128,719,414,619,619,414,719,128,256,1774,1002,1710,

%U 2995,1710,1002,1774,256,512,4389,2398,4894,11977,11977,4894,2398,4389,512,1024

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2....4.....8.....16.......32........64........128..........256

%C ...2....8...21....49....120......293.......719.......1774.........4389

%C ...4...21...28....75....174......414......1002.......2398.........5743

%C ...8...49...75...204....619.....1710......4894......14053........40063

%C ..16..120..174...619...2995....11977.....48677.....201771.......826524

%C ..32..293..414..1710..11977....73031....432088....2685906.....16394959

%C ..64..719.1002..4894..48677...432088...3646656...32938897....290133839

%C .128.1774.2398.14053.201771..2685906..32938897..442204876...5767984330

%C .256.4389.5743.40063.826524.16394959.290133839.5767984330.110715247064

%H R. H. Hardin, <a href="/A316518/b316518.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5

%F k=3: a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +a(n-4) -a(n-5) for n>8

%F k=4: [order 10] for n>13

%F k=5: [order 25] for n>28

%F k=6: [order 44] for n>49

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A303721.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 05 2018