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A316801 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 5
0, 0, 0, 0, 3, 0, 0, 4, 4, 0, 0, 9, 8, 9, 0, 0, 18, 15, 15, 18, 0, 0, 33, 31, 49, 31, 33, 0, 0, 72, 92, 170, 170, 92, 72, 0, 0, 133, 264, 581, 792, 581, 264, 133, 0, 0, 278, 784, 2184, 3759, 3759, 2184, 784, 278, 0, 0, 541, 2378, 7680, 18897, 32193, 18897, 7680, 2378, 541, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
.0...0....0.....0......0........0.........0..........0...........0
.0...3....4.....9.....18.......33........72........133.........278
.0...4....8....15.....31.......92.......264........784........2378
.0...9...15....49....170......581......2184.......7680.......28315
.0..18...31...170....792.....3759.....18897......91138......476043
.0..33...92...581...3759....32193....213931....1526824....11680344
.0..72..264..2184..18897...213931...1964108...19450547...202140736
.0.133..784..7680..91138..1526824..19450547..268526785..3980862756
.0.278.2378.28315.476043.11680344.202140736.3980862756.85266493095
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -6*a(n-4) +4*a(n-5) for n>6
k=3: [order 15] for n>18
k=4: [order 65] for n>66
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..1..1..1..1. .1..1..0..1. .1..0..1..1. .1..1..0..1. .1..0..1..1
..1..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
..0..1..0..1. .0..0..1..1. .0..0..1..0. .1..1..0..1. .0..1..0..0
..0..1..1..0. .1..0..0..0. .1..0..0..1. .0..1..1..0. .0..1..1..1
CROSSREFS
Column 2 is A304257.
Column 3 is A305218.
Column 4 is A305219.
Sequence in context: A240455 A304263 A305223 * A143044 A350789 A361357
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 14 2018
STATUS
approved

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Last modified March 4 01:40 EST 2024. Contains 370522 sequences. (Running on oeis4.)