A298093 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 7 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, 92, 45, 92, 53, 177, 21, 34, 359, 77, 149, 87, 87, 149, 77, 359, 34, 55, 705, 111, 250, 150, 171, 150, 250, 111, 705, 55, 89, 1351, 171, 426

Offset: 1

Author

R. H. Hardin, Jan 12 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..92.149.250.426..809.1456.2602.4606..8096.14731.27112.49118

..3..23..21..53..45..87.150.216.249..423..711..980.1560..2431..3368..5598..8655

..5..49..33..92..87.171.203.328.484..782.1106.1905.2833..4428..7210.11516.17938

..8..95..53.149.150.203.229.365.410..734..917.1484.2077..2943..4659..7326.10594

.13.177..77.250.216.328.365.417.593..783.1086.1490.1929..2529..3490..4795..6787

.21.359.111.426.249.484.410.593.822.1041.1437.2208.3116..4525..6831.10816.16439

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1055

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297852.

Column 3 is A297853.

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 35] for n>40

k=5: [order 82] for n>86