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A301951
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
12
0, 1, 0, 1, 2, 0, 2, 5, 5, 0, 3, 16, 20, 13, 0, 5, 52, 123, 83, 34, 0, 8, 169, 680, 947, 342, 89, 0, 13, 549, 4070, 9084, 7326, 1411, 233, 0, 21, 1784, 23565, 98839, 120815, 56710, 5820, 610, 0, 34, 5797, 138014, 1029960, 2406169, 1608681, 439078, 24007, 1597, 0
OFFSET
1,5
COMMENTS
Table starts
.0....1.....1........2..........3............5...............8
.0....2.....5.......16.........52..........169.............549
.0....5....20......123........680.........4070...........23565
.0...13....83......947.......9084........98839.........1029960
.0...34...342.....7326.....120815......2406169........45013365
.0...89..1411....56710....1608681.....58609226......1969215107
.0..233..5820...439078...21418808...1427656268.....86143630040
.0..610.24007..3399722..285190208..34776685046...3768464135104
.0.1597.99026.26323903.3797277789.847137052736.164856325277648
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 4*a(n-1) +a(n-2) -2*a(n-3)
k=4: a(n) = 9*a(n-1) -8*a(n-2) -14*a(n-3) +4*a(n-4) +4*a(n-5) -a(n-6)
k=5: [order 13] for n>15
k=6: [order 26] for n>28
k=7: [order 43] for n>47
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
n=3: [order 10] for n>12
n=4: [order 36] for n>40
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .0..1..0..1
..0..0..0..0. .1..1..0..0. .0..0..1..1. .0..0..1..0. .0..0..1..0
..1..1..1..1. .1..0..0..1. .1..1..1..1. .0..0..0..0. .1..1..0..0
..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1
CROSSREFS
Column 2 is A001519.
Row 1 is A000045(n-1).
Row 2 is A232317(n-1).
Sequence in context: A133394 A305628 A094721 * A144529 A319498 A349782
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 29 2018
STATUS
approved