A297506 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 2, 1, 4, 10, 1, 7, 31, 29, 1, 12, 68, 110, 87, 1, 21, 218, 314, 531, 280, 1, 37, 729, 1829, 2281, 2534, 876, 1, 65, 2097, 8803, 23348, 14201, 11405, 2735, 1, 114, 6139, 34757, 191192, 270845, 88808, 53175, 8583, 1, 200, 18932, 157673, 1247716, 3624914

Offset

1,2

Comments

Table starts

.1.....2.......4........7.........12...........21.............37

.1....10......31.......68........218..........729...........2097

.1....29.....110......314.......1829.........8803..........34757

.1....87.....531.....2281......23348.......191192........1247716

.1...280....2534....14201.....270845......3624914.......35049871

.1...876...11405....88808....3075264.....66289769......978288822

.1..2735...53175...573119...35919085...1272836591....28914051279

.1..8583..246040..3613793..414559944..23896899569...823340493402

.1.26900.1135117.22999331.4794512057.450529429259.23748019543354

Links

R. H. Hardin, Table of n, a(n) for n = 1..242

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)

k=3: [order 11]

k=4: [order 18]

k=5: [order 50]

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -6*a(n-4) -8*a(n-5)

n=3: [order 10]

n=4: [order 24]

n=5: [order 59]

Example

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

Crossrefs

Column 2 is A295525.

Row 1 is A005251(n+2).

Sequence in context: A137634 A100229 A071949 * A297720 A297654 A220922

Adjacent sequences: A297503 A297504 A297505 * A297507 A297508 A297509

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 31 2017

Status

approved