A204609 Number of (n+1) X 2 0..1 arrays with the determinants of 2 X 2 subblocks nondecreasing rightwards and downwards.

16, 47, 125, 335, 907, 2470, 6740, 18406, 50278, 137354, 375250, 1025194, 2800874, 7652122, 20905978, 57116186, 156044314, 426320986, 1164730586, 3182103130, 8693667418, 23751541082, 64890416986, 177283916122, 484348666202

Offset

1,1

Comments

Column 1 of A204616.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-3) for n>6.

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

G.f.: (16 - x - 16*x^2 - 8*x^3 - 4*x^4 - x^5) / ((1 - x)*(1 - 2*x - 2*x^2)).

a(n) = (112 + (193-113*sqrt(3))*(1-sqrt(3))^n + (1+sqrt(3))^n*(193+113*sqrt(3))) / 24 for n>2.

(End)

Example

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

Crossrefs

Cf. A204616.

Sequence in context: A204800 A194268 A292171 * A233063 A208634 A333602

Adjacent sequences: A204606 A204607 A204608 * A204610 A204611 A204612

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved