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A301884
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
13
1, 2, 2, 3, 5, 4, 5, 10, 13, 8, 8, 18, 29, 34, 16, 13, 35, 58, 95, 89, 32, 21, 74, 125, 203, 289, 233, 64, 34, 154, 331, 510, 673, 917, 610, 128, 55, 317, 823, 1754, 1961, 2340, 2841, 1597, 256, 89, 658, 2086, 5463, 8829, 7869, 7883, 8921, 4181, 512, 144, 1370, 5269
OFFSET
1,2
COMMENTS
Table starts
...1....2.....3.....5......8......13.......21........34.........55..........89
...2....5....10....18.....35......74......154.......317........658........1370
...4...13....29....58....125.....331......823......2086.......5269.......13305
...8...34....95...203....510....1754.....5463.....16452......49611......153498
..16...89...289...673...1961....8829....33853....122356.....439781.....1684392
..32..233...917..2340...7869...46079...223869....981222....4188971....19744757
..64..610..2841..7883..31173..240222..1454613...7734317...39492565...231010966
.128.1597..8921.27175.124795.1258853..9620565..62334085..380963915..2762447554
.256.4181.27801.92411.497909.6603593.63336647.498835686.3652793090.32938593566
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = a(n-1) +6*a(n-2) +2*a(n-3)
k=4: a(n) = a(n-1) +12*a(n-2) -2*a(n-3) -38*a(n-4) +a(n-5) +12*a(n-6) -a(n-8)
k=5: [order 7] for n>9
k=6: [order 32] for n>33
k=7: [order 52] for n>54
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7)
n=3: [order 24] for n>25
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..1..1..1. .0..0..1..0. .0..0..1..0
..1..0..0..1. .0..1..0..1. .0..1..0..0. .1..0..0..1. .1..0..1..0
..0..1..0..1. .0..1..0..1. .0..1..1..1. .1..0..1..0. .1..0..1..1
..0..1..0..1. .0..0..0..1. .0..1..0..1. .1..0..1..0. .1..0..0..1
..0..1..0..0. .1..1..0..1. .0..1..1..1. .1..1..1..0. .1..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A001519(n+1).
Row 1 is A000045(n+1).
Sequence in context: A301790 A301964 A334043 * A302081 A209147 A355059
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 28 2018
STATUS
approved