A296320 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

1, 2, 2, 3, 6, 3, 4, 11, 11, 4, 6, 27, 32, 27, 6, 9, 60, 96, 96, 60, 9, 13, 132, 295, 434, 295, 132, 13, 19, 301, 902, 1970, 1970, 902, 301, 19, 28, 669, 2747, 8470, 12547, 8470, 2747, 669, 28, 41, 1502, 8380, 37431, 77426, 77426, 37431, 8380, 1502, 41, 60, 3370, 25577

Offset: 1

Author

R. H. Hardin, Dec 10 2017

Keywords

• nonn
• tabl

Comments

Table starts

..1....2.....3......4........6.........9..........13...........19............28

..2....6....11.....27.......60.......132.........301..........669..........1502

..3...11....32.....96......295.......902........2747.........8380.........25577

..4...27....96....434.....1970......8470.......37431.......164807........723019

..6...60...295...1970....12547.....77426......490668......3078638......19343899

..9..132...902...8470....77426....676269.....6069953.....54182821.....482859661

.13..301..2747..37431...490668...6069953....78105580....994666167...12644605701

.19..669..8380.164807..3078638..54182821...994666167..18043360170..326902733082

.28.1502.25577.723019.19343899.482859661.12644605701.326902733082.8435284786616

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..544

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A184884(n+1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3)

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

k=3: a(n) = a(n-1) +4*a(n-2) +6*a(n-3) +3*a(n-4) -3*a(n-6) +a(n-7) -3*a(n-9) +a(n-11)

k=4: [order 21]

k=5: [order 43]

k=6: [order 85]