login
A298240
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
8
1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 22, 42, 1, 1, 127, 124, 124, 127, 1, 1, 389, 409, 1156, 409, 389, 1, 1, 1192, 1921, 8117, 8117, 1921, 1192, 1, 1, 3645, 8908, 66626, 107163, 66626, 8908, 3645, 1, 1, 11161, 41933, 563826, 1636306, 1636306, 563826, 41933
OFFSET
1,5
COMMENTS
Table starts
.1.....1......1........1..........1.............1...............1
.1.....5.....13.......42........127...........389............1192
.1....13.....22......124........409..........1921............8908
.1....42....124.....1156.......8117.........66626..........563826
.1...127....409.....8117.....107163.......1636306........25784604
.1...389...1921....66626....1636306......45356726......1300110664
.1..1192...8908...563826...25784604....1300110664.....67668568376
.1..3645..41933..4788445..403231105...36992129471...3503621681315
.1.11161.204016.41239301.6388232748.1065292018400.183337397269876
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) with g.f. (1-x^2-x^3)/(1-x-5*x^2-4*x^3).
k=3: [order 13] for n>15
k=4: [order 47] for n>49
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..1
..0..1..0..0. .1..1..0..0. .1..1..0..0. .1..1..0..1. .1..0..1..0
..1..1..0..1. .0..0..1..0. .1..0..1..1. .0..1..0..0. .1..1..0..0
..1..0..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..0. .1..1..0..0
..0..0..0..1. .0..0..1..0. .0..0..0..0. .1..1..0..1. .1..1..0..0
CROSSREFS
Sequence in context: A176487 A272644 A157177 * A299366 A299135 A299893
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 15 2018
STATUS
approved