A250791 Number of (n+1) X (2+1) 0..1 arrays with nondecreasing min(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.

24, 66, 180, 490, 1336, 3646, 9956, 27194, 74288, 202950, 554460, 1514802, 4138504, 11306590, 30890164, 84393482, 230567264, 629921462, 1720977420, 4701797730, 12845550264, 35094695950, 95880492388, 261950376634, 715661738000

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) + 2*a(n-4).

Conjectures from Colin Barker, Nov 20 2018: (Start)

G.f.: 2*x*(12 - 15*x - 6*x^2 + 8*x^3) / ((1 - x)^2*(1 - 2*x - 2*x^2)).

a(n) = (-6 + (39-23*sqrt(3))*(1-sqrt(3))^n + 39*(1+sqrt(3))^n + 23*sqrt(3)*(1+sqrt(3))^n + 6*n) / 9.

(End)

Example

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

Crossrefs

Column 2 of A250797.

Sequence in context: A347314 A175153 A250799 * A043154 A039331 A043934

Adjacent sequences: A250788 A250789 A250790 * A250792 A250793 A250794

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved