VOOZH about

URL: https://oeis.org/A283572

⇱ A283572 - OEIS

login
A283572
T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
13
0, 0, 0, 1, 4, 0, 2, 26, 16, 0, 5, 72, 169, 68, 0, 12, 282, 674, 1108, 256, 0, 26, 908, 4313, 6812, 6453, 924, 0, 56, 2832, 21186, 67892, 60802, 36038, 3232, 0, 118, 8856, 104464, 509952, 945100, 528436, 194173, 11044, 0, 244, 26750, 513458, 3890056, 10919674
OFFSET
1,5
COMMENTS
Table starts
.0......0........1..........2............5.............12...............26
.0......4.......26.........72..........282............908.............2832
.0.....16......169........674.........4313..........21186...........104464
.0.....68.....1108.......6812........67892.........509952..........3890056
.0....256.....6453......60802.......945100.......10919674........129527524
.0....924....36038.....528436.....12699250......226897932.......4173039716
.0...3232...194173....4441052....164714523.....4558585174.....129997769458
.0..11044..1021432...36589848...2089140956....89724600000....3965206666608
.0..37104..5275885..296555892..26034179747..1736716820366..118919078661476
.0.122984.26869458.2373574616.320066184088.33188681249924.3520469545329364
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8)
k=3: [order 12]
k=4: [order 16]
k=5: [order 42]
k=6: [order 54]
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)
n=2: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)
n=3: [order 12]
n=4: [order 16]
n=5: [order 42]
n=6: [order 64]
EXAMPLE
Some solutions for n=4, k=4
..1..1..0..0. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..1..0
..1..0..0..1. .0..0..0..1. .1..1..0..0. .1..0..0..0. .0..1..1..0
..0..0..1..0. .0..1..0..1. .1..0..1..0. .0..0..1..1. .1..0..0..0
..0..0..0..0. .0..1..1..0. .0..0..1..0. .1..0..0..1. .0..0..1..1
CROSSREFS
Column 2 is A283036.
Row 1 is A073778(n-1).
Sequence in context: A346492 A145877 A373984 * A057075 A281653 A327305
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 11 2017
STATUS
approved