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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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 16 2012
STATUS
approved

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Last modified June 18 14:18 EDT 2024. Contains 373481 sequences. (Running on oeis4.)