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A302150
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
11
1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 2, 4, 1, 16, 1, 3, 5, 10, 1, 32, 1, 6, 11, 17, 28, 1, 64, 1, 10, 34, 56, 65, 84, 1, 128, 1, 21, 88, 255, 289, 257, 260, 1, 256, 1, 42, 271, 1038, 2005, 1529, 1025, 816, 1, 512, 1, 86, 798, 4771, 12212, 15999, 8152, 4097, 2576, 1, 1024, 1, 179
OFFSET
1,3
COMMENTS
Table starts
...1.1....1.....1......1.......1.........1..........1............1
...2.1....2.....2......3.......6........10.........21...........42
...4.1....4.....5.....11......34........88........271..........798
...8.1...10....17.....56.....255......1038.......4771........21866
..16.1...28....65....289....2005.....12212......83092.......578398
..32.1...84...257...1529...15999....145150....1482725.....15902462
..64.1..260..1025...8152..128319...1728734...26544210....439103633
.128.1..816..4097..43676.1030709..20614702..476725579..12181287002
.256.1.2576.16385.234707.8283143.245896061.8575073202.338788296901
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = a(n-1)
k=3: a(n) = 4*a(n-1) -2*a(n-2) -2*a(n-3)
k=4: a(n) = 5*a(n-1) -4*a(n-2) for n>3
k=5: [order 12]
k=6: [order 7] for n>9
k=7: [order 51] for n>54
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
n=3: [order 25] for n>27
n=4: [order 85] for n>89
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..1..1
..1..1..1..1. .1..1..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..0
..0..1..1..0. .1..1..1..1. .0..1..1..0. .0..1..1..0. .1..1..1..0
..0..1..1..1. .0..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..1..1..0. .1..1..1..0. .1..1..1..0. .1..1..1..0. .0..1..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 4 is A052539(n-2).
Row 2 is A240513(n-3).
Sequence in context: A208482 A199856 A301906 * A193554 A372701 A131350
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 02 2018
STATUS
approved