|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|