|
| |
|
|
A302889
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
|
|
12
|
|
|
|
1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 37, 3, 16, 1, 72, 53, 141, 6, 32, 1, 168, 197, 238, 569, 10, 64, 1, 496, 818, 2278, 1102, 2262, 21, 128, 1, 1296, 2548, 12782, 20937, 5570, 8968, 42, 256, 1, 3616, 10926, 98458, 200186, 206332, 28594, 35667, 86, 512, 1, 9760, 42671
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Table starts
...1..1......1......1.........1...........1.............1...............1
...2..2.....12.....20........72.........168...........496............1296
...4..2.....37.....53.......197.........818..........2548...........10926
...8..3....141....238......2278.......12782.........98458..........714934
..16..6....569...1102.....20937......200186.......2727690........37626360
..32.10...2262...5570....206332.....3452246......89290791......2247650354
..64.21...8968..28594...2059835....60501563....2899297652....133518102376
.128.42..35667.149206..20622709..1073161270...94799190457...7977498513759
.256.86.141839.788373.206851726.19073141368.3098646840396.476377988322833
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 10]
k=4: [order 35] for n>37
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
n=3: [order 16] for n>17
n=4: [order 51] for n>54
|
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..0..0..0. .0..1..1..0
..1..1..1..0. .1..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..1..1
..0..1..1..0. .0..1..1..0. .0..1..1..1. .1..0..0..1. .0..1..1..1
..0..1..1..0. .0..1..1..1. .1..1..1..0. .0..0..0..0. .1..1..1..0
..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..0..0..1. .1..1..1..0
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
