A210054 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one, two or four distinct values, and new values 0..3 introduced in row major order.

9, 51, 323, 2187, 15435, 111659, 819243, 6058155, 44991659, 334914219, 2496201387, 18617371307, 138903833259, 1036559854251, 7736058194603, 57739004914347, 430954921634475, 3216631813810859, 24009028665518763, 179204877435185835

Offset

1,1

Comments

Column 1 of A210061.

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 48*a(n-2) + 52*a(n-3) - 16*a(n-4).

Conjectures from Colin Barker, Jul 14 2018: (Start)

G.f.: x*(9 - 66*x + 92*x^2 - 32*x^3) / ((1 - x)*(1 - 4*x)*(1 - 8*x + 4*x^2)).

a(n) = (1/3) + 4^n - (1/6)*(4-2*sqrt(3))^n*(-2+sqrt(3)) + (1/3)*2^(-1+n)*(2+sqrt(3))^(1+n).

(End)

Example

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

Crossrefs

Cf. A210061.

Sequence in context: A155617 A126477 A275861 * A272393 A231748 A181161

Adjacent sequences: A210051 A210052 A210053 * A210055 A210056 A210057

Keyword

nonn

Author

R. H. Hardin, Mar 16 2012

Status

approved