login
A299721
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
7
1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 46, 42, 1, 1, 127, 246, 246, 127, 1, 1, 389, 1205, 2545, 1205, 389, 1, 1, 1192, 6354, 23877, 23877, 6354, 1192, 1, 1, 3645, 33804, 242107, 439647, 242107, 33804, 3645, 1, 1, 11161, 182056, 2501312, 8668148, 8668148
OFFSET
1,5
COMMENTS
Table starts
.1.....1......1.........1...........1..............1................1
.1.....5.....13........42.........127............389.............1192
.1....13.....46.......246........1205...........6354............33804
.1....42....246......2545.......23877.........242107..........2501312
.1...127...1205.....23877......439647........8668148........174287007
.1...389...6354....242107.....8668148......330958005......12889348273
.1..1192..33804...2501312...174287007....12889348273.....971255866215
.1..3645.182056..26078075..3523382014...504002310677...73433529818762
.1.11161.988181.273889895.71647565308.19818564264619.5581654300729422
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +5*a(n-2) +4*a(n-3)
k=3: [order 12] for n>14
k=4: [order 29] for n>30
k=5: [order 83] for n>86
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..0. .0..0..0..0. .0..1..1..1. .0..0..1..1
..1..1..1..1. .1..1..1..0. .0..0..0..1. .0..0..1..0. .1..0..0..1
..0..1..1..1. .0..0..0..1. .1..1..1..1. .1..1..0..0. .0..0..1..1
..0..0..0..0. .0..0..1..1. .1..0..1..0. .0..1..0..0. .0..0..1..1
..0..1..0..0. .1..0..1..0. .1..1..1..1. .1..1..0..1. .0..1..1..1
CROSSREFS
Column 2 is A298234.
Sequence in context: A299893 A299060 A299821 * A300342 A119725 A239279
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 17 2018
STATUS
approved