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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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 08:17 EST 2021. Contains 349627 sequences. (Running on oeis4.)