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

Author

R. H. Hardin, Mar 24 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A240513(n-2).

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]