A301608 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 6, 8, 8, 6, 1, 1, 10, 13, 25, 13, 10, 1, 1, 21, 26, 65, 65, 26, 21, 1, 1, 42, 55, 226, 330, 226, 55, 42, 1, 1, 86, 154, 755, 1297, 1297, 755, 154, 86, 1, 1, 179, 356, 2539, 6393, 8888, 6393, 2539, 356, 179, 1, 1, 370, 884, 8794, 30904

Offset

1,5

Comments

Table starts

.1..1...1....1......1.......1........1..........1...........1............1

.1..2...2....3......6......10.......21.........42..........86..........179

.1..2...2....8.....13......26.......55........154.........356..........884

.1..3...8...25.....65.....226......755.......2539........8794........30539

.1..6..13...65....330....1297.....6393......30904......154041.......764894

.1.10..26..226...1297....8888....60841.....421168.....2940940.....20639456

.1.21..55..755...6393...60841...591585....5880829....58383932....585233819

.1.42.154.2539..30904..421168..5880829...83224304..1180228568..16849867573

.1.86.356.8794.154041.2940940.58383932.1180228568.23865691820.485485211198

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

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

k=3: [order 18]

k=4: [order 66]

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..1. .0..1..0..1. .0..0..0..0. .0..0..1..1
..0..0..1..1. .1..1..0..1. .1..0..1..0. .0..1..0..0. .0..0..1..1
..1..1..0..0. .1..0..1..1. .0..1..0..1. .0..0..1..0. .0..0..1..1
..1..1..0..0. .1..1..1..0. .1..0..1..0. .1..0..0..0. .0..1..0..0
..1..1..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..0. .0..0..0..0

Crossrefs

Column 2 is A240513(n-2).

Sequence in context: A317815 A318423 A318091 * A285521 A187451 A134542

Adjacent sequences: A301605 A301606 A301607 * A301609 A301610 A301611

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 24 2018

Status

approved