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R. H. Hardin, <a href="/A283543/b283543.txt">Table of n, a(n) for n = 1..313</a>

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T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors.

2, 4, 4, 7, 11, 8, 13, 27, 33, 16, 24, 76, 127, 98, 32, 44, 201, 578, 573, 291, 64, 81, 537, 2369, 4089, 2615, 865, 128, 149, 1444, 10069, 25532, 29558, 11903, 2570, 256, 274, 3859, 42664, 167920, 282773, 212441, 54211, 7637, 512, 504, 10339, 179733, 1094959

1,1

Table starts

....2.....4.......7........13..........24............44..............81

....4....11......27........76.........201...........537............1444

....8....33.....127.......578........2369.........10069...........42664

...16....98.....573......4089.......25532........167920.........1094959

...32...291....2615.....29558......282773.......2905717........29377334

...64...865...11903....212441.....3109801......49760703.......778500603

..128..2570...54211...1529463....34266804.....854841910.....20707472573

..256..7637..246869..11006233...377393657...14672363665....550220030803

..512.22693.1124239..79212552..4156954825..251901309671..14624495679716

.1024.67432.5119755.570077446.45786939720.4324419947902.388675661283840

Empirical for column k:

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

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

k=3: a(n) = 5*a(n-1) -a(n-2) -7*a(n-3) +10*a(n-4) +4*a(n-5) -8*a(n-6)

k=4: [order 8]

k=5: [order 21]

k=6: [order 27]

k=7: [order 59]

Empirical for row n:

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

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

n=3: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) -6*a(n-4) +11*a(n-5) -2*a(n-6)

n=4: [order 8]

n=5: [order 21]

n=6: [order 32]

n=7: [order 69]

Some solutions for n=4 k=4

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

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

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

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

Column 1 is A000079.

Column 2 is A282990.

Row 1 is A000073(n+3).

Row 2 is A282641.

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nonn,tabl

R. H. Hardin, Mar 10 2017

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