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A301450 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 171, 108, 16, 32, 401, 1008, 1008, 401, 32, 64, 1490, 5930, 9541, 5930, 1490, 64, 128, 5536, 34976, 91370, 91370, 34976, 5536, 128, 256, 20569, 206266, 877044, 1423344, 877044, 206266, 20569, 256, 512, 76424, 1216562 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1.....2.......4.........8..........16............32...............64

...2.....8......29.......108.........401..........1490.............5536

...4....29.....171......1008........5930.........34976...........206266

...8...108....1008......9541.......91370........877044..........8414314

..16...401....5930.....91370.....1423344......22207589........346263718

..32..1490...34976....877044....22207589.....564002959......14319674594

..64..5536..206266...8414314...346263718...14319674594.....592006690060

.128.20569.1216562..80726964..5399605493..363595763125...24472344492129

.256.76424.7175157.774477323.84198470831.9231743942243.1011614229196954

LINKS

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

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

k=3: [order 13]

k=4: [order 40]

EXAMPLE

Some solutions for n=5 k=4

..0..0..0..1. .0..1..1..1. .0..1..0..1. .0..1..1..1. .0..0..0..1

..1..0..1..0. .0..1..0..0. .1..0..1..0. .1..0..0..0. .0..1..0..0

..1..0..1..1. .1..0..0..0. .0..1..0..1. .1..0..1..1. .1..1..0..1

..0..1..0..1. .1..1..0..1. .0..0..1..0. .1..0..1..0. .0..1..0..1

..1..1..0..0. .1..1..0..1. .0..1..1..1. .1..0..0..1. .1..1..0..1

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A220547.

Sequence in context: A300472 A326105 A300811 * A302265 A302965 A302808

Adjacent sequences:  A301447 A301448 A301449 * A301451 A301452 A301453

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 21 2018

STATUS

approved

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Last modified January 29 01:54 EST 2020. Contains 331328 sequences. (Running on oeis4.)