A265987 Number of n X 3 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

2, 2, 6, 10, 30, 66, 182, 442, 1166, 2930, 7590, 19306, 49662, 126882, 325526, 833050, 2135150, 5467346, 14007942, 35877322, 91909086, 235418370, 603054710, 1544728186, 3956947022, 10135859762, 25963647846, 66507086890, 170361678270

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Jan 09 2019: (Start)

G.f.: 2*x*(1 + x)*(1 - 2*x) / ((1 - x)*(1 - x - 4*x^2)).

a(n) = 1 + (-((1-sqrt(17))/2)^n + ((1+sqrt(17))/2)^n) / sqrt(17).

(End)

Example

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

Crossrefs

Column 3 of A265991.

Sequence in context: A229733 A383494 A051765 * A076907 A260785 A153897

Adjacent sequences: A265984 A265985 A265986 * A265988 A265989 A265990

Keyword

nonn

Author

R. H. Hardin, Dec 19 2015

Status

approved