A267946 Number of n X 1 0..2 arrays with every repeated value in every row and column one larger mod 3 than the previous repeated value, and upper left element zero.

1, 3, 8, 21, 53, 132, 323, 783, 1880, 4485, 10637, 25116, 59075, 138519, 323936, 755877, 1760453, 4093620, 9506051, 22049055, 51091496, 118287237, 273658877, 632714892, 1462080131, 3377002023, 7796796848, 17994911781, 41519520053

Offset

1,2

Comments

Column 1 of A267952.

Links

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

Formula

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

Conjectures from Colin Barker, Mar 21 2018: (Start)

G.f.: x*(1 - 2*x^2) / ((1 - 2*x)*(1 - x - 3*x^2)).

a(n) = 2^(-n)*(-39*4^n + (26-7*sqrt(13))*(1-sqrt(13))^n + (1+sqrt(13))^n*(26+7*sqrt(13))) / 39.

(End)

Example

Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..2....1....1....2....0....2....1....1....1....2....0....2....2....0....1....2
..1....2....0....0....2....1....0....2....2....1....2....2....0....2....2....0
..1....0....1....2....0....0....1....0....0....0....0....0....2....1....2....2
..0....1....1....1....2....2....0....1....2....1....2....0....0....2....0....0
..1....1....0....2....1....0....0....0....0....2....1....1....2....1....0....1
..0....2....2....1....2....2....2....0....1....1....0....2....2....1....1....2
..2....2....1....0....1....1....1....2....0....0....1....0....0....0....0....2

Crossrefs

Cf. A267952.

Sequence in context: A014396 A170881 A039671 * A166287 A186812 A027930

Adjacent sequences: A267943 A267944 A267945 * A267947 A267948 A267949

Keyword

nonn

Author

R. H. Hardin, Jan 22 2016

Status

approved