A304544 - OEIS

%I #4 May 14 2018 08:43:15

%S 1,2,2,3,5,3,5,7,7,5,8,17,9,17,8,13,35,19,19,35,13,21,61,37,70,37,61,

%T 21,34,127,65,124,124,65,127,34,55,265,129,328,461,328,129,265,55,89,

%U 507,275,808,949,949,808,275,507,89,144,1013,555,2265,2792,2558,2792,2265

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

%C Table starts

%C ..1...2...3....5.....8.....13......21.......34.......55........89........144

%C ..2...5...7...17....35.....61.....127......265......507......1013.......2071

%C ..3...7...9...19....37.....65.....129......275......555......1143.......2417

%C ..5..17..19...70...124....328.....808.....2265.....6025.....17221......50786

%C ..8..35..37..124...461....949....2792....10838....31286....102740.....377657

%C .13..61..65..328...949...2558....9840....40134...152679....664967....2951738

%C .21.127.129..808..2792...9840...53098...285622..1415123...8070788...46626298

%C .34.265.275.2265.10838..40134..285622..1991764.12087446..88143119..641080685

%C .55.507.555.6025.31286.152679.1415123.12087446.96472384.894904467.8247056696

%H R. H. Hardin, <a href="/A304544/b304544.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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

%F k=3: [order 13]

%F k=4: [order 67] for n>68

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303802.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 14 2018