A301531 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 16, 24, 16, 1, 1, 40, 92, 92, 40, 1, 1, 113, 391, 742, 391, 113, 1, 1, 304, 1728, 5472, 5472, 1728, 304, 1, 1, 833, 7640, 43211, 74479, 43211, 7640, 833, 1, 1, 2270, 33824, 339956, 1050609, 1050609, 339956, 33824, 2270, 1, 1, 6194, 150119

Offset

1,5

Comments

Table starts

.1....1......1........1..........1............1..............1

.1....3......5.......16.........40..........113............304

.1....5.....24.......92........391.........1728...........7640

.1...16.....92......742.......5472........43211.........339956

.1...40....391.....5472......74479......1050609.......14890200

.1..113...1728....43211....1050609.....26709523......681538595

.1..304...7640...339956...14890200....681538595....31363814530

.1..833..33824..2691202..212169356..17470755574..1449439465725

.1.2270.150119.21316797.3027488635.448475800823.67069319310675

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -a(n-6)

k=3: [order 20] for n>21

k=4: [order 60] for n>62

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..1..1..1. .0..0..0..1. .0..0..1..0
..0..1..1..0. .1..1..1..1. .1..1..1..0. .0..0..1..1. .0..0..0..0
..1..1..1..0. .0..0..0..1. .1..0..0..0. .0..0..1..1. .1..1..1..1
..0..0..0..1. .0..1..0..1. .0..0..1..1. .1..1..1..1. .1..1..1..1
..0..0..1..1. .0..0..1..1. .0..1..1..0. .1..1..1..1. .0..1..1..0

Crossrefs

Column 2 is A300533.

Sequence in context: A300539 A300966 A300923 * A158418 A124925 A073145

Adjacent sequences: A301528 A301529 A301530 * A301532 A301533 A301534

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 23 2018

Status

approved