A296039 - OEIS

%I #4 Dec 03 2017 07:38:23

%S 1,1,1,1,5,1,1,11,11,1,1,21,31,21,1,1,55,70,70,55,1,1,125,251,204,251,

%T 125,1,1,271,799,997,997,799,271,1,1,645,2266,4102,8472,4102,2266,645,

%U 1,1,1479,7005,15399,51941,51941,15399,7005,1479,1,1,3325,21780,63267

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2 or 4 king-move neighboring 1s.

%C Table starts

%C .1....1.....1......1........1.........1..........1............1.............1

%C .1....5....11.....21.......55.......125........271..........645..........1479

%C .1...11....31.....70......251.......799.......2266.........7005.........21780

%C .1...21....70....204......997......4102......15399........63267........258493

%C .1...55...251....997.....8472.....51941.....285366......1853852......11570787

%C .1..125...799...4102....51941....472540....3650122.....33758793.....307234618

%C .1..271..2266..15399...285366...3650122...39608385....518787061....6686146382

%C .1..645..7005..63267..1853852..33758793..518787061..10042412853..188033223758

%C .1.1479.21780.258493.11570787.307234618.6686146382.188033223758.5131681923323

%H R. H. Hardin, <a href="/A296039/b296039.txt">Table of n, a(n) for n = 1..240</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-1) +6*a(n-3) +4*a(n-5)

%F k=3: [order 11]

%F k=4: [order 17]

%F k=5: [order 55]

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 03 2017