|
| |
|
|
A227333
|
|
T(n,k) = Number of n X k 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X (k+1) binary array having two adjacent 1's and two adjacent 0's, with rows and columns of the latter in lexicographically nondecreasing order.
|
|
6
|
|
|
|
2, 4, 4, 8, 11, 8, 15, 34, 34, 15, 26, 104, 153, 104, 26, 42, 285, 708, 708, 285, 42, 64, 683, 3013, 4917, 3013, 683, 64, 93, 1469, 11292, 33297, 33297, 11292, 1469, 93, 130, 2906, 37312, 204206, 366606, 204206, 37312, 2906, 130, 176, 5383, 110816, 1108382
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Table starts
...2....4......8.......15.........26..........42..........64..........93
...4...11.....34......104........285.........683........1469........2906
...8...34....153......708.......3013.......11292.......37312......110816
..15..104....708.....4917......33297......204206.....1108382.....5361624
..26..285...3013....33297.....366606.....3774137....35026386...290742258
..42..683..11292...204206....3774137....66730314..1084271645.15918049450
..64.1469..37312..1108382...35026386..1084271645.31357593706
..93.2906.110816..5361624..290742258.15918049450
.130.5383.301923.23477312.2174611745
|
|
|
LINKS
|
R. H. Hardin, Table of n, a(n) for n = 1..97
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = (1/6)*n^3 + (5/6)*n + 1.
k=2: [polynomial of degree 7] for n>2.
k=3: [polynomial of degree 15] for n>6.
k=4: [polynomial of degree 31] for n>10.
|
|
|
EXAMPLE
|
Some solutions for n=4, k=4
..0..0..0..0....0..1..0..1....0..1..0..0....0..1..0..1....0..0..1..0
..0..0..1..0....0..1..0..1....0..1..1..1....1..0..1..0....0..0..0..1
..0..0..0..0....1..0..0..1....1..0..1..1....0..1..0..0....0..0..0..0
..1..0..0..0....1..1..1..0....0..0..0..0....1..0..0..1....1..0..0..0
|
|
|
CROSSREFS
|
Column 1 is A000125.
Sequence in context: A265204 A073420 A034408 * A223317 A027131 A338986
Adjacent sequences: A227330 A227331 A227332 * A227334 A227335 A227336
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
R. H. Hardin Jul 07 2013
|
|
|
STATUS
|
approved
|
| |
|
|
