A296952 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

1, 2, 2, 3, 8, 3, 4, 16, 16, 4, 6, 36, 45, 36, 6, 9, 112, 135, 135, 112, 9, 13, 256, 544, 620, 544, 256, 13, 19, 608, 1765, 3637, 3637, 1765, 608, 19, 28, 1680, 5763, 17450, 37179, 17450, 5763, 1680, 28, 41, 4064, 20811, 86139, 256713, 256713, 86139, 20811, 4064

Offset: 1

Author

R. H. Hardin, Dec 22 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

..2....8....16......36.......112........256..........608..........1680

..3...16....45.....135.......544.......1765.........5763.........20811

..4...36...135.....620......3637......17450........86139........451210

..6..112...544....3637.....37179.....256713......1898178......16087936

..9..256..1765...17450....256713....2640993.....29067775.....356242817

.13..608..5763...86139...1898178...29067775....482228052....8786244680

.19.1680.20811..451210..16087936..356242817...8786244680..246430289779

.28.4064.70207.2267574.121741279.4007327435.148081034460.6194343019644

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Column 1 is A000930(n+1).

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +8*a(n-3) -12*a(n-4)

k=3: [order 19]

k=4: [order 46]