A282862 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

Offset

1,1

Comments

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

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]

Example

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

Crossrefs

Column 1 is A000073(n+3).

Sequence in context: A268781 A282647 A269089 * A296578 A268750 A282996

Adjacent sequences: A282859 A282860 A282861 * A282863 A282864 A282865

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 23 2017

Status

approved