A233106 Number of n X 1 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

1, 2, 6, 23, 99, 452, 2136, 10313, 50469, 249062, 1235466, 6147803, 30650439, 152986472, 764135196, 3818284493, 19084248009, 95399716682, 476934013326, 2384476356383, 11921800651179, 59607259863692, 298031069141856

Offset

1,2

Comments

Column 1 of A233113.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 23*a(n-2) + 15*a(n-3).

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

G.f.: x*(1 - 7*x + 11*x^2) / ((1 - x)*(1 - 3*x)*(1 - 5*x)).

a(n) = (75 + 10*3^n + 3*5^n) / 120.

(End)

Example

Some solutions for n=7:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....0....1....0....1....1....1....0....1....1....0....1....0....1
..2....2....0....1....5....1....5....2....1....1....5....5....1....0....1....2
..1....4....1....5....1....5....2....0....1....5....1....5....2....4....2....5
..5....0....1....1....1....4....0....3....5....5....1....1....1....2....1....5
..1....2....2....0....2....5....3....5....1....2....1....0....5....4....3....2
..5....2....0....1....5....4....1....2....0....5....5....0....2....2....3....5

Crossrefs

Sequence in context: A242586 A196018 A009449 * A133656 A078487 A193038

Adjacent sequences: A233103 A233104 A233105 * A233107 A233108 A233109

Keyword

nonn

Author

R. H. Hardin, Dec 04 2013

Status

approved