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A300930
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 37, 75, 37, 3, 5, 129, 508, 508, 129, 5, 8, 450, 3447, 6638, 3447, 450, 8, 13, 1568, 23404, 87561, 87561, 23404, 1568, 13, 21, 5464, 158855, 1155263, 2244335, 1155263, 158855, 5464, 21, 34, 19041, 1078231, 15238332
OFFSET
1,5
COMMENTS
Table starts
..0.....1.......1..........2............3...............5..................8
..1.....3......11.........37..........129.............450...............1568
..1....11......75........508.........3447...........23404.............158855
..2....37.....508.......6638........87561.........1155263...........15238332
..3...129....3447......87561......2244335........57594572.........1477281166
..5...450...23404....1155263.....57594572......2875574552.......143498589629
..8..1568..158855...15238332...1477281166....143498589629.....13930396115571
.13..5464.1078231..200997959..37892542998...7160975085336...1352339873296663
.21.19041.7318522.2651226860.971951600750.357354070296570.131283287305824217
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4) for n>5
k=3: [order 8] for n>10
k=4: [order 26] for n>27
k=5: [order 64] for n>67
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..1. .0..1..1..1. .0..0..1..0. .0..0..1..1. .0..0..1..0
..0..1..0..1. .0..1..0..0. .1..1..0..0. .0..0..1..0. .0..1..0..0
..0..1..0..1. .1..1..0..0. .0..0..1..0. .0..0..1..0. .0..1..1..0
..1..1..1..0. .1..1..1..1. .1..1..0..0. .0..0..1..1. .1..1..1..1
..1..0..0..0. .1..0..0..1. .1..0..0..0. .1..1..1..1. .1..0..0..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A232031(n-1).
Sequence in context: A180771 A300546 A300973 * A109528 A136125 A092580
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 15 2018
STATUS
approved