A304010 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 27, 26, 27, 49, 1, 1, 99, 53, 64, 64, 53, 99, 1, 1, 194, 99, 115, 137, 115, 99, 194, 1, 1, 387, 197, 211, 271, 271, 211, 197, 387, 1, 1, 773, 371, 439, 655, 538, 655, 439, 371, 773, 1, 1, 1538, 713, 870

Offset: 1

Author

R. H. Hardin, May 04 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

.1...4...7..13...26...49....99...194....387....773....1538....3081.....6147

.1...7..13..21...27...53....99...197....371....713....1365....2645.....5105

.1..13..21..26...64..115...211...439....870...1725....3513....7141....14372

.1..26..27..64..137..271...655..1412...3245...7809...17290...40682....93292

.1..49..53.115..271..538..1458..2973...7826..19113...47074..115148...283156

.1..99..99.211..655.1458..4224.10633..28365..75175..201031..544217..1452266

.1.194.197.439.1412.2973.10633.30468..84398.254233..751747.2193664..6512888

.1.387.371.870.3245.7826.28365.84398.264104.857398.2706019.8591303.27513653

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

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

k=3: [order 16] for n>17

k=4: [order 67] for n>70