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A250610
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 x(i,j)-x(i-1,j) in the j direction.
1
1013, 2336, 4353, 7320, 11749, 18664, 30113, 50192, 87093, 157200, 293281, 560872, 1091045, 2145944, 4249857, 8451360, 16847605, 33632896, 67195841, 134313656, 268540773, 536986056, 1073867233, 2147619760, 4295114549, 8590093424
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
Conjectures from Colin Barker, Nov 15 2018: (Start)
G.f.: x*(1013 - 2729*x + 1790*x^2 - 512*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 15 2018
a(n) = 128 + 2^(7+n) + 410*n + 219*n^2.
(End)
EXAMPLE
Some solutions for n=6:
..1..0..1..1..1..1..0..0....1..1..1..1..1..1..1..0....1..1..1..1..0..1..0..0
..1..0..1..1..1..1..0..0....1..1..1..1..1..1..1..1....1..1..1..1..0..1..0..0
..1..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0
..1..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0
..0..0..1..1..1..1..0..1....1..1..1..1..1..1..1..1....1..1..1..1..0..1..0..0
..0..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0
..0..0..1..1..1..1..0..1....1..1..1..1..1..1..1..1....1..1..1..1..0..1..1..1
CROSSREFS
Column 7 of A250611.
Sequence in context: A157008 A161404 A252634 * A126239 A120214 A251267
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 26 2014
STATUS
approved