A250784 Number of (2+1) X (n+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.

18, 46, 106, 238, 518, 1106, 2326, 4838, 9978, 20446, 41686, 84658, 171398, 346166, 697786, 1404398, 2823078, 5669266, 11375926, 22812358, 45722618, 91603646, 183463606, 367341938, 735354918, 1471795606, 2945348026, 5893538638

Offset

1,1

Links

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

Formula

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

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

G.f.: 2*x*(9 - 13*x - 3*x^2 + 8*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)).

a(n) = 2^(1-n) * (2^n*(1+11*2^n) + 2*(1-sqrt(5))^n*(-2+sqrt(5)) - 2*(1+sqrt(5))^n*(2+sqrt(5))).

(End)

Example

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

Crossrefs

Row 2 of A250783.

Sequence in context: A057444 A130414 A108642 * A250731 A353209 A203596

Adjacent sequences: A250781 A250782 A250783 * A250785 A250786 A250787

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved