A250778 Number of (n+1) X (3+1) 0..1 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.

46, 106, 230, 482, 990, 2010, 4054, 8146, 16334, 32714, 65478, 131010, 262078, 524218, 1048502, 2097074, 4194222, 8388522, 16777126, 33554338, 67108766, 134217626, 268435350, 536870802, 1073741710, 2147483530, 4294967174

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

Conjectures from Colin Barker, Nov 19 2018: (Start)

G.f.: 2*x*(23 - 39*x + 18*x^2) / ((1 - x)^2*(1 - 2*x)).

a(n) = 2^(5+n) - 4*n - 14.

(End)

Example

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

Crossrefs

Column 3 of A250783.

Sequence in context: A248529 A204769 A333040 * A118620 A044233 A044614

Adjacent sequences: A250775 A250776 A250777 * A250779 A250780 A250781

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved