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.

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

R. H. Hardin, Table of n, a(n) for n = 1..180

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

Adjacent sequences: A298237 A298238 A298239 * A298241 A298242 A298243

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 15 2018

Status

approved