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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. 1
9, 51, 323, 2187, 15435, 111659, 819243, 6058155, 44991659, 334914219, 2496201387, 18617371307, 138903833259, 1036559854251, 7736058194603, 57739004914347, 430954921634475, 3216631813810859, 24009028665518763, 179204877435185835 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 9 19:08 EDT 2020. Contains 333362 sequences. (Running on oeis4.)