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A243513 Number of length n+2 0..4 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..4 introduced in 0..4 order. 1
3, 5, 10, 24, 65, 187, 552, 1646, 4927, 14769, 44294, 132868, 398589, 1195751, 3587236, 10761690, 32285051, 96855133, 290565378, 871696112, 2615088313, 7845264915, 23535794720, 70607384134, 211822152375, 635466457097 (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) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).

Conjectures from Colin Barker, Nov 02 2018: (Start)

G.f.: x*(3 - 10*x + 6*x^2) / ((1 - x)^2*(1 - 3*x)).

a(n) = (7 + 3^n + 2*n) / 4.

(End)

EXAMPLE

All solutions for n=3:

..0....0....0....0....0....0....0....0....0....0

..1....0....1....0....0....1....1....1....0....0

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

..3....1....0....2....0....0....3....3....0....2

..0....2....1....3....1....3....1....4....0....0

CROSSREFS

Column 4 of A243519.

Sequence in context: A209001 A240619 A171867 * A002039 A243514 A243515

Adjacent sequences:  A243510 A243511 A243512 * A243514 A243515 A243516

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 05 2014

STATUS

approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)