A250789 Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

576, 1596, 4054, 10306, 25126, 59590, 137082, 307762, 676266, 1460260, 3107536, 6535280, 13611742, 28129720, 57764876, 118015794, 240116940, 486922786, 984765176, 1987317314, 4003558184, 8054089024, 16184388422, 32492334224

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 8*a(n-1) - 25*a(n-2) + 35*a(n-3) - 9*a(n-4) - 37*a(n-5) + 47*a(n-6) - 15*a(n-7) - 10*a(n-8) + 9*a(n-9) - 2*a(n-10).

Empirical g.f.: 2*x*(288 - 1506*x + 2843*x^2 - 1193*x^3 - 3324*x^4 + 5009*x^5 - 1866*x^6 - 1087*x^7 + 1094*x^8 - 256*x^9) / ((1 - x)^6*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

Example

Some solutions for n=4:
..1..0..0..0..0....1..0..0..1..0....0..0..1..0..1....0..0..0..0..0
..1..0..0..0..0....1..0..0..1..0....0..0..1..0..1....0..0..0..0..0
..1..0..0..0..1....1..0..0..1..0....0..0..1..0..1....0..0..0..0..0
..1..0..0..0..1....1..0..1..0..1....0..1..0..1..0....0..0..0..0..0
..1..0..0..1..0....1..0..1..0..1....0..1..0..1..1....0..0..0..0..1
..1..0..0..1..0....1..0..1..0..1....0..1..0..1..1....0..0..0..1..0
..1..0..1..0..1....1..1..0..1..0....0..1..0..1..1....0..1..1..0..1
..1..1..0..1..0....1..1..0..1..1....0..1..0..1..1....0..1..1..0..1

Crossrefs

Row 7 of A250783.

Sequence in context: A254848 A235181 A268773 * A137484 A189990 A064254

Adjacent sequences: A250786 A250787 A250788 * A250790 A250791 A250792

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved