A250857 Number of (5+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

54410, 291165, 1043885, 2955136, 7134786, 15344785, 30214465, 55486360, 96292546, 159461501, 253855485, 390738440, 584174410, 851456481, 1213566241, 1695663760, 2327608090, 3144508285, 4187304941, 5503382256, 7147210610

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..176

Formula

Empirical: a(n) = (763/18)*n^6 + (1949/3)*n^5 + (136493/36)*n^4 + (72691/6)*n^3 + (693923/36)*n^2 + (43319/3)*n + 4096.

Conjectures from Colin Barker, Nov 21 2018: (Start)

G.f.: x*(54410 - 89705*x + 148340*x^2 - 141944*x^3 + 83994*x^4 - 28671*x^5 + 4096*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=1:
..2..2....2..2....1..1....3..3....3..3....3..3....2..1....3..3....3..2....0..1
..3..3....0..1....3..3....0..1....3..3....3..3....0..1....3..3....1..1....1..2
..2..2....0..1....3..3....2..3....3..3....3..3....0..1....2..2....2..3....1..2
..2..2....0..1....1..1....0..1....2..2....0..0....0..1....1..1....0..1....1..2
..0..1....1..3....3..3....2..3....2..2....1..1....2..3....0..1....1..2....0..1
..0..2....1..3....1..1....2..3....0..1....2..2....0..3....0..2....0..3....0..2

Crossrefs

Row 5 of A250853.

Sequence in context: A270763 A251479 A203624 * A083616 A235104 A205997

Adjacent sequences: A250854 A250855 A250856 * A250858 A250859 A250860

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved