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A268255 Number of length-(n+1) 0..2 arrays with new repeated values introduced in sequential order starting with zero. 1
7, 17, 42, 106, 273, 717, 1918, 5218, 14413, 40349, 114282, 326938, 943257, 2740797, 8010982, 23529346, 69385813, 205282157, 608959218, 1810358938, 5391414273, 16078923309, 48007516942, 143470822498, 429083952157, 1284051486077 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 7*a(n-1) - 15*a(n-2) + 7*a(n-3) + 6*a(n-4).

Conjectures from Colin Barker, Jan 11 2019: (Start)

G.f.: x*(7 - 32*x + 28*x^2 + 18*x^3) / ((1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)).

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

(End)

EXAMPLE

Some solutions for n=8:

..0....1....1....0....0....1....0....0....2....1....0....1....2....0....0....1

..0....0....0....0....0....0....0....2....0....2....1....2....1....1....0....0

..2....0....0....2....0....1....1....0....0....0....2....1....2....0....1....2

..0....1....0....0....2....0....0....0....0....0....1....2....1....0....0....0

..1....1....1....1....0....2....0....0....1....2....2....0....0....2....0....2

..0....1....2....1....2....0....1....1....1....1....1....0....1....1....1....1

..1....1....1....0....0....0....0....0....1....0....2....1....0....0....1....0

..0....1....2....1....2....2....2....0....2....1....0....0....0....1....1....0

..2....1....0....0....1....1....1....1....2....0....0....2....1....1....1....1

CROSSREFS

Column 2 of A268261.

Sequence in context: A184862 A194772 A193546 * A124965 A253973 A200080

Adjacent sequences:  A268252 A268253 A268254 * A268256 A268257 A268258

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 29 2016

STATUS

approved

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Last modified June 15 08:14 EDT 2021. Contains 345048 sequences. (Running on oeis4.)