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R. H. Hardin, <a href="/A282862/b282862.txt">Table of n, a(n) for n = 1..364</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, vertical and antidiagonal neighbors.

2, 4, 4, 7, 11, 7, 13, 31, 31, 13, 24, 89, 131, 89, 24, 44, 251, 583, 583, 251, 44, 81, 715, 2562, 4163, 2562, 715, 81, 149, 2028, 11250, 28537, 28537, 11250, 2028, 149, 274, 5761, 49471, 197892, 305430, 197892, 49471, 5761, 274, 504, 16358, 217459, 1369929

1,1

Table starts

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

...4....11......31........89.........251...........715............2028

...7....31.....131.......583........2562.........11250...........49471

..13....89.....583......4163.......28537........197892.........1369929

..24...251....2562.....28537......305430.......3303160........35681883

..44...715...11250....197892.....3303160......55930891.......945547378

..81..2028...49471...1369929....35681883.....945547378.....25000646212

.149..5761..217459...9480913...385325426...15974465522....660597156170

.274.16358..955873..65635874..4161954773..270001575386..17464365749979

.504.46452.4201865.454328733.44951001482.4562926495008.461623512113494

Empirical for column k:

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

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

k=3: [order 11]

k=4: [order 21]

k=5: [order 43]

k=6: [order 85]

Some solutions for n=4 k=4

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

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

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

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

Column 1 is A000073(n+3).

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nonn,tabl

R. H. Hardin, Feb 23 2017

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