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A298508
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.
7
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, 148, 301, 1, 1, 864, 493, 1297, 1297, 493, 864, 1, 1, 2485, 2093, 6063, 10969, 6063, 2093, 2485, 1, 1, 7144, 8047, 35908, 86979, 86979, 35908, 8047, 7144, 1, 1, 20541, 31951
OFFSET
1,5
COMMENTS
Table starts
.1....1.....1.......1........1..........1............1.............1
.1....5....12......37......104........301..........864..........2485
.1...12....10......50......148........493.........2093..........8047
.1...37....50.....269.....1297.......6063........35908........203345
.1..104...148....1297....10969......86979.......795788.......7018070
.1..301...493....6063....86979....1091801.....16092678.....225171354
.1..864..2093...35908...795788...16092678....364785216....7961618817
.1.2485..8047..203345..7018070..225171354...7961618817..269830709761
.1.7144.31951.1189795.62968846.3223061387.177727031452.9389112358693
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 5*a(n-2) +8*a(n-3) +4*a(n-4)
k=3: [order 16] for n>18
k=4: [order 58] for n>61
EXAMPLE
Some solutions for n=5, k=4
..0..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..0..0. .0..1..1..0
..1..1..1..1. .0..0..0..0. .1..1..1..1. .1..0..0..1. .1..1..1..1
..1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
..0..1..1..0. .0..1..1..0. .0..1..1..0. .1..1..1..1. .1..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..1. .1..0..1..1. .0..0..0..0
CROSSREFS
Column 2 is A297909.
Sequence in context: A110522 A146987 A297915 * A298328 A299221 A300035
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 20 2018
STATUS
approved