|
|
A250655
|
|
Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
|
|
1
|
|
|
81, 169, 345, 697, 1401, 2809, 5625, 11257, 22521, 45049, 90105, 180217, 360441, 720889, 1441785, 2883577, 5767161, 11534329, 23068665, 46137337, 92274681, 184549369, 369098745, 738197497, 1476395001, 2952790009, 5905580025
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*49 + (5*2^(n-1)-1)*7 +2^(n+1).
Empirical g.f.: x*(81 - 74*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 15 2018
|
|
EXAMPLE
|
Some solutions for n=4:
..1..1..0..0..0..0..0..0....1..1..1..1..0..0..0..0....1..1..1..1..0..0..0..0
..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....1..1..1..1..1..1..1..1
..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....1..1..1..1..1..1..1..1
..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....0..0..0..0..0..1..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|