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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045(n+1)

Sequence in context: A029093 A369788 A301541 * A318037 A326165 A078462

Adjacent sequences: A240516 A240517 A240518 * A240520 A240521 A240522

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 06 2014

Status

approved