A298508 - OEIS

%I #6 May 17 2023 12:15:55

%S 1,1,1,1,5,1,1,12,12,1,1,37,10,37,1,1,104,50,50,104,1,1,301,148,269,

%T 148,301,1,1,864,493,1297,1297,493,864,1,1,2485,2093,6063,10969,6063,

%U 2093,2485,1,1,7144,8047,35908,86979,86979,35908,8047,7144,1,1,20541,31951

%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C .1....5....12......37......104........301..........864..........2485

%C .1...12....10......50......148........493.........2093..........8047

%C .1...37....50.....269.....1297.......6063........35908........203345

%C .1..104...148....1297....10969......86979.......795788.......7018070

%C .1..301...493....6063....86979....1091801.....16092678.....225171354

%C .1..864..2093...35908...795788...16092678....364785216....7961618817

%C .1.2485..8047..203345..7018070..225171354...7961618817..269830709761

%C .1.7144.31951.1189795.62968846.3223061387.177727031452.9389112358693

%H R. H. Hardin, <a href="/A298508/b298508.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 16] for n>18

%F k=4: [order 58] for n>61

%e Some solutions for n=5, k=4

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

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

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

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

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

%Y Column 2 is A297909.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 20 2018