A250900 Number of (2+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.

125, 431, 1325, 3867, 11029, 31215, 88421, 251819, 722525, 2089551, 6088189, 17854683, 52646213, 155906639, 463263029, 1380089259, 4119295693, 12312797679, 36841923341, 110320248347, 330524536565, 990650861871, 2970006427525

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 40*a(n-2) + 82*a(n-3) - 91*a(n-4) + 52*a(n-5) - 12*a(n-6).

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

G.f.: x*(125 - 819*x + 2015*x^2 - 2393*x^3 + 1392*x^4 - 324*x^5) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x)).

a(n) = 23/2 - 2^(4+n) + (7*3^(2+n))/2 + 2*n + 3*2^(3+n)*n + n^2.

(End)

Example

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

Crossrefs

Row 2 of A250898.

Sequence in context: A045184 A059470 A316387 * A293040 A250136 A141480

Adjacent sequences: A250897 A250898 A250899 * A250901 A250902 A250903

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved