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A302367 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 13
1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 31, 3, 16, 1, 72, 20, 109, 6, 32, 1, 168, 154, 77, 397, 10, 64, 1, 496, 284, 918, 209, 1430, 21, 128, 1, 1296, 1109, 3125, 6580, 774, 5110, 42, 256, 1, 3616, 3472, 21831, 26458, 49293, 3143, 18395, 86, 512, 1, 9760, 12763, 125193 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Table starts

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

...2..2....12....20.......72.......168.........496..........1296

...4..2....31....20......154.......284........1109..........3472

...8..3...109....77......918......3125.......21831........125193

..16..6...397...209.....6580.....26458......405340.......3462040

..32.10..1430...774....49293....330505.....9361759.....134269527

..64.21..5110..3143...367512...3858625...188443738....4558781926

.128.42.18395.13556..2856621..48375470..4174802035..169314399506

.256.86.66203.60280.22185382.608124211.91302504318.6186362081201

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 50] for n>53

Empirical for row n:

n=1: a(n) = a(n-1)

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

n=3: [order 16] for n>18

n=4: [order 63] for n>66

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Sequence in context: A302212 A302460 A303242 * A303084 A302889 A303624

Adjacent sequences:  A302364 A302365 A302366 * A302368 A302369 A302370

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 06 2018

STATUS

approved

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Last modified November 12 22:10 EST 2019. Contains 329079 sequences. (Running on oeis4.)