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A300472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 160, 108, 16, 32, 401, 925, 925, 401, 32, 64, 1490, 5363, 8608, 5363, 1490, 64, 128, 5536, 31106, 80914, 80914, 31106, 5536, 128, 256, 20569, 180397, 759100, 1231578, 759100, 180397, 20569, 256, 512, 76424, 1046223 (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.....160.......925........5363.........31106..........180397

...8...108.....925......8608.......80914........759100.........7121067

..16...401....5363.....80914.....1231578......18735889.......284885784

..32..1490...31106....759100....18735889.....462538206.....11408562672

..64..5536..180397...7121067...284885784...11408562672....456303004550

.128.20569.1046223..66808673..4332278363..281433652906..18253046515989

.256.76424.6067629.626787854.65881928079.6942908646999.730219136878799

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..264

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: a(n) = 6*a(n-1) -a(n-2) -a(n-3) +a(n-4) -4*a(n-5) +a(n-6) -a(n-7)

k=4: [order 22]

k=5: [order 58] for n>59

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A220547.

Sequence in context: A318016 A320402 A208709 * A326105 A300811 A301450

Adjacent sequences:  A300469 A300470 A300471 * A300473 A300474 A300475

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 06 2018

STATUS

approved

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Last modified August 18 16:51 EDT 2022. Contains 356215 sequences. (Running on oeis4.)