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URL: https://oeis.org/A297595

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A297595
T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.
12
1, 2, 1, 3, 5, 1, 4, 9, 9, 1, 6, 13, 25, 20, 1, 9, 33, 49, 69, 41, 1, 13, 69, 145, 154, 205, 85, 1, 19, 121, 443, 752, 577, 597, 178, 1, 28, 253, 1141, 3145, 3747, 1977, 1701, 369, 1, 41, 529, 3009, 10131, 23066, 18577, 6962, 4949, 769, 1, 60, 1013, 8455, 37929, 103673
OFFSET
1,2
COMMENTS
Table starts
.1...2.....3.....4.......6........9........13..........19...........28
.1...5.....9....13......33.......69.......121.........253..........529
.1...9....25....49.....145......443......1141........3009.........8455
.1..20....69...154.....752.....3145.....10131.......37929.......150388
.1..41...205...577....3747....23066....103673......514290......2834897
.1..85...597..1977...18577...163704....975485.....6551844.....50398161
.1.178..1701..6962...93150..1172288...9403199....85828150....919035936
.1.369..4949.24441..464697..8419996..90862063..1120526916..16723808887
.1.769.14389.85803.2320289.60354437.875241087.14592832760.303459238317
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)
k=3: a(n) = a(n-1) +2*a(n-2) +10*a(n-3) +4*a(n-4) -8*a(n-5) -8*a(n-6)
k=4: [order 9]
k=5: [order 22]
k=6: [order 40]
k=7: [order 83]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3)
n=2: a(n) = a(n-1) +4*a(n-3)
n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +7*a(n-4) -8*a(n-6) -6*a(n-7)
n=4: [order 12]
n=5: [order 26]
n=6: [order 49]
EXAMPLE
Some solutions for n=6 k=4
..0..0..0..0. .0..1..0..0. .1..0..0..0. .1..0..0..0. .0..0..1..0
..0..1..1..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0
..0..0..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
..0..1..0..1. .0..0..1..1. .1..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..1. .0..0..0..0. .1..0..0..0. .0..0..0..0. .1..0..0..0
..0..0..0..1. .1..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..0..0
CROSSREFS
Column 2 is A105309(n+1).
Row 1 is A000930(n+1).
Row 2 is A089977(n+1).
Sequence in context: A188211 A175009 A297395 * A049069 A030237 A210557
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 01 2018
STATUS
approved