A250901 Number of (3+1) X (n+1) 0..2 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.

413, 1450, 4388, 12387, 33821, 91030, 244200, 657443, 1784205, 4894210, 13588116, 38193131, 108619621, 312200310, 905600200, 2647025819, 7785177061, 23009431986, 68264323652, 203115146611, 605677397453, 1809046090230

Offset

1,1

Links

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

Formula

Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).

Empirical g.f.: x*(413 - 4332*x + 19193*x^2 - 47217*x^3 + 70990*x^4 - 67269*x^5 + 39526*x^6 - 13236*x^7 + 1944*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 23 2018

Example

Some solutions for n=4:
..0..1..1..1..1....2..1..0..1..0....2..2..2..0..0....2..2..0..1..1
..0..1..1..1..1....1..0..1..2..1....2..2..2..1..1....2..2..1..2..2
..0..1..1..1..1....1..0..1..2..2....2..2..2..1..1....1..1..0..1..1
..0..1..1..2..2....1..0..1..2..2....1..1..1..0..2....0..0..1..2..2

Crossrefs

Row 3 of A250898.

Sequence in context: A282127 A344119 A257823 * A205755 A331825 A250945

Adjacent sequences: A250898 A250899 A250900 * A250902 A250903 A250904

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved