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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A184884(n+1).

Sequence in context: A272958 A290632 A291543 * A296396 A125102 A003506

Adjacent sequences: A296317 A296318 A296319 * A296321 A296322 A296323

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 10 2017

Status

approved