A250902 Number of (4+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.

1333, 4750, 14196, 39003, 102789, 265546, 680504, 1742387, 4479925, 11612686, 30445732, 80928947, 218431629, 598934874, 1667663960, 4709666459, 13467918413, 38924144238, 113481270292, 333163706923, 983467807413, 2915295816330

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*(1333 - 13912*x + 61001*x^2 - 147893*x^3 + 218694*x^4 - 204317*x^5 + 119174*x^6 - 39804*x^7 + 5832*x^8) /((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 23 2018

Example

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

Crossrefs

Row 4 of A250898.

Sequence in context: A043613 A028501 A183646 * A250946 A145494 A234264

Adjacent sequences: A250899 A250900 A250901 * A250903 A250904 A250905

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved