A304479 - OEIS

%I #4 May 13 2018 10:49:03

%S 1,2,2,4,4,4,8,12,12,8,16,24,19,24,16,32,64,37,37,64,32,64,184,94,110,

%T 94,184,64,128,432,202,297,297,202,432,128,256,1088,428,869,931,869,

%U 428,1088,256,512,2944,965,2325,2870,2870,2325,965,2944,512,1024,7360,2134

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

%C Table starts

%C ...1....2....4.....8....16.....32......64......128......256.......512

%C ...2....4...12....24....64....184.....432.....1088.....2944......7360

%C ...4...12...19....37....94....202.....428......965.....2134......4692

%C ...8...24...37...110...297....869....2325.....6379....17568.....48401

%C ..16...64...94...297...931...2870....8058....25040....76568....231646

%C ..32..184..202...869..2870..11079...35462...133597...471114...1710896

%C ..64..432..428..2325..8058..35462..132348...573938..2341508...9662652

%C .128.1088..965..6379.25040.133597..573938..2942145.13964485..67899747

%C .256.2944.2134.17568.76568.471114.2341508.13964485.77098563.429574178

%H R. H. Hardin, <a href="/A304479/b304479.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6

%F k=3: [order 12] for n>13

%F k=4: [order 65] for n>67

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303794.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 13 2018