A250801 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing min(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.

140, 490, 1430, 3776, 9258, 21610, 48600, 106426, 228342, 482496, 1007546, 2084962, 4284032, 8754018, 17810278, 36111264, 73018218, 147325946, 296740456, 596862762, 1199199990, 2407260800, 4828861690, 9680929586, 19399411088

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 9*a(n-3) + 9*a(n-4) + 6*a(n-5) - 8*a(n-6) -a(n-7) + 2*a(n-8).

Empirical g.f.: 2*x*(70 - 35*x - 125*x^2 + 148*x^3 + 82*x^4 - 125*x^5 - 15*x^6 + 32*x^7) / ((1 - x)^3*(1 + x)^2*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

Example

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

Crossrefs

Row 4 of A250797.

Sequence in context: A242319 A010080 A350210 * A184386 A184378 A180294

Adjacent sequences: A250798 A250799 A250800 * A250802 A250803 A250804

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved