|
|
A202458
|
|
Number of (n+2) X 7 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.
|
|
1
|
|
|
1728, 4137, 9338, 19614, 38478, 71088, 124740, 209445, 338596, 529731, 805398, 1194128, 1731522, 2461458, 3437424, 4723983, 6398376, 8552269, 11293650, 14748882, 19064918, 24411684, 30984636, 39007497, 48735180, 60456903, 74499502
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/840)*n^7 + (3/40)*n^6 + (47/30)*n^5 + 16*n^4 + (10847/120)*n^3 + (11557/40)*n^2 + (258737/420)*n + 715.
G.f.: x*(1728 - 9687*x + 24626*x^2 - 36022*x^3 + 32318*x^4 - 17650*x^5 + 5408*x^6 - 715*x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
|
|
EXAMPLE
|
Some solutions for n=4:
..0..0..0..0..1..1..0....0..0..0..0..0..1..0....0..0..0..0..0..0..0
..0..0..0..0..1..1..1....0..0..0..0..1..1..0....0..0..0..0..0..0..0
..0..0..0..1..1..1..1....0..0..0..0..1..1..1....0..0..0..0..0..0..0
..0..0..0..1..1..1..1....1..1..1..1..1..1..1....0..0..0..0..1..1..0
..0..0..1..1..1..1..1....1..1..1..1..1..1..1....0..0..1..1..1..1..1
..0..0..0..1..1..1..1....0..0..1..1..1..1..1....0..1..1..1..1..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|