A297858 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 21, 30, 21, 49, 8, 13, 95, 33, 53, 53, 33, 95, 13, 21, 177, 53, 90, 45, 90, 53, 177, 21, 34, 359, 77, 145, 81, 81, 145, 77, 359, 34, 55, 705, 111, 244, 130, 131, 130, 244, 111, 705, 55, 89, 1351, 171, 406

Offset: 1

Author

R. H. Hardin, Jan 07 2018

Keywords

• nonn
• tabl

Comments

Table starts

..0...1...1...2...3...5...8..13..21..34...55...89..144...233...377...610...987

..1...3...7..13..23..49..95.177.359.705.1351.2689.5303.10321.20423.40353.79223

..1...7..15..19..21..33..53..77.111.171..269..415..643..1013..1605..2543..4041

..2..13..19..30..53..90.145.244.406.771.1396.2472.4358..7688.13953.25626.46458

..3..23..21..53..45..81.130.186.203.313..533..737.1132..1722..2282..3719..5672

..5..49..33..90..81.131.146.252.320.522..705.1188.1654..2554..4086..6240..9384

..8..95..53.145.130.146.181.289.294.594..711.1167.1681..2374..3827..6129..8841

.13.177..77.244.186.252.289.298.406.568..780.1009.1299..1639..2169..2986..4144

.21.359.111.406.203.320.294.406.430.614..791.1026.1413..1823..2395..3684..5064

Examples

			Some solutions for n=7 k=4
..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..0..1..0. .0..0..1..0
..1..1..0..0. .0..1..0..0. .0..0..1..0. .1..0..1..0. .1..1..1..0
..1..0..1..0. .0..1..1..1. .1..1..1..0. .1..0..0..1. .0..1..0..1
..1..1..0..0. .1..0..1..0. .0..0..1..1. .0..1..0..1. .0..1..0..1
..0..0..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1. .0..1..0..1
..1..0..0..0. .1..1..0..1. .0..0..0..1. .1..0..1..0. .0..1..0..1
..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1104

Crossrefs

Column 1 is A000045(n-1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6

k=3: a(n) = 2*a(n-1) -a(n-4) -a(n-5) -a(n-6) +a(n-7) +a(n-8) for n>9

k=4: [order 32] for n>37

k=5: [order 76] for n>81