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

1,5

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297852.

Column 3 is A297853.

Sequence in context: A135338 A084602 A297858 * A298055 A298888 A298660

Adjacent sequences: A298090 A298091 A298092 * A298094 A298095 A298096

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 12 2018

Status

approved