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A243516
Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order.
1
3, 5, 10, 25, 77, 280, 1156, 5267, 25915, 135214, 736706, 4139833, 23767897, 138468212, 814675840, 4824766303, 28699128503, 171207852154, 1023332115838, 6124430348357, 36684624841813, 219860794899520, 1318179574171580
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 17*a(n-1) - 111*a(n-2) + 355*a(n-3) - 584*a(n-4) + 468*a(n-5) - 144*a(n-6).
Conjectures from Colin Barker, Nov 02 2018: (Start)
G.f.: x*(3 - 46*x + 258*x^2 - 655*x^3 + 739*x^4 - 288*x^5) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)).
a(n) = (2722 + 675*2^n + 25*2^(1+2*n) + 50*3^(1+n) + 2^n*3^(1+n) + 660*n) / 1800.
(End)
EXAMPLE
All solutions for n=3:
..0....0....0....0....0....0....0....0....0....0
..0....0....0....1....0....1....1....1....0....1
..1....0....0....2....1....2....2....2....0....2
..2....0....1....3....2....3....0....3....0....0
..3....1....2....0....0....4....3....1....0....1
CROSSREFS
Column 7 of A243519.
Sequence in context: A002039 A243514 A243515 * A243517 A243518 A025486
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jun 05 2014
STATUS
approved