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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 10:18 EDT 2021. Contains 347584 sequences. (Running on oeis4.)