A304019 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 38, 45, 3, 5, 120, 103, 103, 120, 5, 8, 333, 281, 370, 281, 333, 8, 13, 928, 826, 1318, 1318, 826, 928, 13, 21, 2613, 2421, 4449, 5162, 4449, 2421, 2613, 21, 34, 7400, 7104, 16187, 20979, 20979, 16187, 7104, 7400, 34, 55, 21053

Offset

1,5

Comments

Table starts

..0....1.....1......2.......3........5........8........13.........21

..1....7....16.....45.....120......333......928......2613.......7400

..1...16....38....103.....281......826.....2421......7104......20732

..2...45...103....370....1318.....4449....16187.....57097.....204138

..3..120...281...1318....5162....20979....87747....363807....1503951

..5..333...826...4449...20979....99733...488944...2363993...11464178

..8..928..2421..16187...87747...488944..2820436..16004647...90893514

.13.2613..7104..57097..363807..2363993.16004647.106817959..709737869

.21.7400.20732.204138.1503951.11464178.90893514.709737869.5516875986

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 20]

k=4: [order 66] for n>67

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A305489 A305089 A316740 * A305367 A304959 A316641

Adjacent sequences: A304016 A304017 A304018 * A304020 A304021 A304022

Keyword

nonn,tabl

Author

R. H. Hardin, May 04 2018

Status

approved