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

1,5

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..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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A186366 A135338 A084602 * A298093 A298055 A298888

Adjacent sequences: A297855 A297856 A297857 * A297859 A297860 A297861

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 07 2018

Status

approved