|
|
A227265
|
|
Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of three or less, with rows and columns of the latter in lexicographically nondecreasing order.
|
|
1
|
|
|
3, 8, 16, 30, 54, 93, 153, 241, 365, 534, 758, 1048, 1416, 1875, 2439, 3123, 3943, 4916, 6060, 7394, 8938, 10713, 12741, 15045, 17649, 20578, 23858, 27516, 31580, 36079, 41043, 46503, 52491, 59040, 66184, 73958, 82398, 91541, 101425, 112089, 123573
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (47/12)*n - 1.
G.f.: x*(3 - 7*x + 6*x^2 - x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
|
|
EXAMPLE
|
Some solutions for n=4:
..1..1....1..1....1..1....1..1....1..0....1..1....1..0....1..1....1..0....1..0
..1..1....1..0....1..0....1..1....0..0....1..1....1..0....1..1....1..0....1..1
..1..0....1..1....1..1....1..1....0..0....1..1....1..1....1..0....0..0....1..1
..1..0....0..1....1..1....1..1....0..0....0..1....1..1....0..0....0..0....0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|