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A320409
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 6, 4, 8, 14, 14, 8, 16, 35, 47, 35, 16, 32, 95, 156, 156, 95, 32, 64, 257, 548, 786, 548, 257, 64, 128, 700, 1970, 3761, 3761, 1970, 700, 128, 256, 1907, 7049, 18725, 27236, 18725, 7049, 1907, 256, 512, 5202, 25364, 92578, 191615, 191615, 92578
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2.....4.......8.......16.........32..........64...........128
...2....6....14......35.......95........257.........700..........1907
...4...14....47.....156......548.......1970........7049.........25364
...8...35...156.....786.....3761......18725.......92578........463045
..16...95...548....3761....27236.....191615.....1353623.......9623424
..32..257..1970...18725...191615....1957026....19677729.....199877194
..64..700..7049...92578..1353623...19677729...282206549....4085687781
.128.1907.25364..463045..9623424..199877194..4085687781...84346447443
.256.5202.91307.2308299.68454701.2025592349.58997871413.1737667793009
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..199
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7)
k=3: [order 23] for n>25
k=4: [order 83] for n>85
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..1..1..0..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .1..0..0..1
..0..1..0..0. .1..0..0..1. .1..1..1..1. .1..0..1..1. .0..0..0..0
..1..0..1..0. .1..1..1..1. .0..0..0..0. .0..1..0..1. .0..0..1..0
..1..1..0..0. .1..1..0..1. .0..0..0..1. .0..0..0..1. .0..1..1..0
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A318018.
Sequence in context: A318075 A318343 A318024 * A096466 A088965 A059474
Adjacent sequences: A320406 A320407 A320408 * A320410 A320411 A320412
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Oct 12 2018
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STATUS
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approved
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