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A305022
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
7
0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 14, 18, 0, 0, 61, 73, 73, 61, 0, 0, 209, 387, 769, 387, 209, 0, 0, 702, 2000, 6742, 6742, 2000, 702, 0, 0, 2381, 10487, 62314, 101178, 62314, 10487, 2381, 0, 0, 8069, 54957, 570806, 1575677, 1575677, 570806, 54957, 8069, 0, 0, 27330
OFFSET
1,5
COMMENTS
Table starts
.0....0......0........0..........0............0...............0
.0....3......5.......18.........61..........209.............702
.0....5.....14.......73........387.........2000...........10487
.0...18.....73......769.......6742........62314..........570806
.0...61....387.....6742.....101178......1575677........24498639
.0..209...2000....62314....1575677.....42306830......1125868355
.0..702..10487...570806...24498639...1125868355.....51145342760
.0.2381..54957..5242925..380995482..30031715172...2330913035532
.0.8069.287218.48153854.5926730196.801023698345.106184262061654
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 15] for n>16
k=4: [order 42] for n>44
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..1
..0..1..0..1. .1..1..1..0. .0..1..1..0. .1..1..1..1. .1..1..0..0
..0..1..1..1. .0..1..0..0. .1..0..1..1. .0..1..1..0. .0..1..0..1
..1..1..1..0. .0..0..1..0. .0..1..0..0. .0..0..1..0. .1..0..1..0
..0..0..1..0. .1..1..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..1
CROSSREFS
Column 2 is A303684.
Sequence in context: A316763 A304065 A305457 * A316686 A304767 A316511
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 23 2018
STATUS
approved