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

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Last modified August 10 13:09 EDT 2022. Contains 356039 sequences. (Running on oeis4.)