A207590 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.
6, 36, 60, 144, 324, 756, 1728, 3996, 9180, 21168, 48708, 112212, 258336, 594972, 1369980, 3154896, 7264836, 16729524, 38524032, 88712604, 204284700, 470422512, 1083276612, 2494544148, 5744373984, 13228006428, 30461128380, 70145147664
Offset: 1
Keywords
Examples
Some solutions for n=4: ..0..1..1..0....1..1..0..0....1..1..0..1....0..1..1..1....1..1..1..1 ..1..0..1..0....1..0..1..0....0..1..1..1....1..0..1..0....1..0..1..0 ..0..1..0..0....0..1..1..0....1..0..1..0....0..1..0..1....0..1..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A207589.
Formula
Empirical: a(n) = a(n-1) + 3*a(n-2) for n>4.
Conjectures from Colin Barker, Mar 05 2018: (Start)
G.f.: 6*x*(1 + 5*x + x^2 - 4*x^3) / (1 - x - 3*x^2).
a(n) = (2^(1-n)*((1-sqrt(13))^n*(-35+13*sqrt(13)) + (1+sqrt(13))^n*(35+13*sqrt(13)))) / (9*sqrt(13)) for n>2.
(End)
Comments