A300966 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 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, 16, 16, 1, 1, 40, 44, 44, 40, 1, 1, 113, 159, 327, 159, 113, 1, 1, 304, 580, 1653, 1653, 580, 304, 1, 1, 833, 2145, 10135, 15861, 10135, 2145, 833, 1, 1, 2270, 8034, 60730, 154497, 154497, 60730, 8034, 2270, 1, 1, 6194, 30017, 366981

Offset

1,5

Comments

Table starts

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

.1....3.....5......16........40.........113..........304............833

.1....5....16......44.......159.........580.........2145...........8034

.1...16....44.....327......1653.......10135........60730.........366981

.1...40...159....1653.....15861......154497......1550025.......15500146

.1..113...580...10135....154497.....2472677.....40689759......667804248

.1..304..2145...60730...1550025....40689759...1111779576....30150922994

.1..833..8034..366981..15500146...667804248..30150922994..1357319826867

.1.2270.30017.2221003.156403068.11028400250.822562611004.61232880680325

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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 22] for n>24

k=4: [order 75] for n>78

Example

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

Crossrefs

Column 2 is A300533.

Sequence in context: A108553 A176700 A300539 * A300923 A301531 A158418

Adjacent sequences: A300963 A300964 A300965 * A300967 A300968 A300969

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 17 2018

Status

approved