A240519 T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order.

1, 2, 2, 3, 3, 3, 5, 6, 6, 5, 8, 10, 10, 10, 8, 13, 21, 28, 28, 21, 13, 21, 42, 73, 99, 73, 42, 21, 34, 86, 196, 326, 326, 196, 86, 34, 55, 179, 515, 1080, 1376, 1080, 515, 179, 55, 89, 370, 1376, 3765, 6205, 6205, 3765, 1376, 370, 89, 144, 770, 3686, 13282, 28942, 37624

Offset: 1

Author

R. H. Hardin, Apr 06 2014

Keywords

• nonn
• tabl

Comments

Table starts

..1...2....3......5.......8.......13.........21..........34...........55

..2...3....6.....10......21.......42.........86.........179..........370

..3...6...10.....28......73......196........515........1376.........3686

..5..10...28.....99.....326.....1080.......3765.......13282........46928

..8..21...73....326....1376.....6205......28942......135093.......636475

.13..42..196...1080....6205....37624.....231665.....1440880......9082172

.21..86..515...3765...28942...231665....1906245....16000486....135790448

.34.179.1376..13282..135093..1440880...16000486...180760099...2056580724

.55.370.3686..46928..636475..9082172..135790448..2056580724..31517059634

.89.770.9914.166611.3024792.57688194.1158315893.23588995330.488025204070

Examples

			Some solutions for n=4 k=4
..0..0..0..1....0..1..1..1....0..1..0..1....0..0..1..0....0..1..0..1
..1..0..1..1....0..0..1..0....1..1..1..0....1..1..1..1....1..0..0..0
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..0....0..1..0..1
..1..0..1..0....1..0..1..0....1..0..0..0....1..0..1..1....1..1..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A000045(n+1)

Formula

Empirical for column k:

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

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

k=3: [order 20]

k=4: [order 48]