|
|
A303040
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
|
|
12
|
|
|
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 14, 10, 16, 13, 31, 28, 35, 21, 32, 21, 113, 56, 74, 71, 42, 64, 34, 363, 150, 234, 197, 186, 86, 128, 55, 813, 360, 869, 703, 544, 459, 179, 256, 89, 1751, 828, 2926, 3069, 2494, 1686, 1287, 370, 512, 144, 5001, 1906, 8500, 11079
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Table starts
...1...2....3.....5......8......13.......21........34.........55..........89
...2...3...11....21.....31.....113......363.......813.......1751........5001
...4...6...14....28.....56.....150......360.......828.......1906........4628
...8..10...35....74....234.....869.....2926......8500......27931.......96592
..16..21...71...197....703....3069....11079.....39281.....147655......574771
..32..42..186...544...2494...13597....59654....251705....1186522.....5869222
..64..86..459..1686...9882...63254...345668...1853428...10924077....67726475
.128.179.1287..5252..38855..298328..2060154..13840842..103929273...827923879
.256.370.3490.16336.158630.1487003.13122422.112389422.1107624272.11716920536
|
|
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 13] for n>16
k=4: [order 70]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 11] for n>12
n=4: [order 61] for n>62
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1
..0..0..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..0
..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .1..1..0..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .0..0..0..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|