A250893 Number of (n+1) X (3+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.

403, 1325, 4388, 14196, 44525, 136509, 412006, 1231112, 3657629, 10837431, 32088956, 95066910, 281997715, 837788285, 2492972738, 7429400340, 22170161033, 66233321571, 198057333352, 592697831402, 1774742767583, 5316672917289

Offset

1,1

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 60*a(n-2) + 162*a(n-3) - 255*a(n-4) + 234*a(n-5) - 116*a(n-6) + 24*a(n-7) for n>9.

Conjectures from Colin Barker, Nov 23 2018: (Start)

G.f.: x*(403 - 3511*x + 12668*x^2 - 24246*x^3 + 25568*x^4 - 13314*x^5 + 1284*x^6 + 1746*x^7 - 594*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).

a(n) = (-8*(179+223*2^n-25*3^(3+n)) + (1104-845*2^n)*n + (32+375*2^n)*n^2) / 32 for n>2.

(End)

Example

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

Crossrefs

Column 3 of A250898.

Sequence in context: A325151 A213605 A083815 * A261857 A165808 A283662

Adjacent sequences: A250890 A250891 A250892 * A250894 A250895 A250896

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved