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A212825
Number of 0..4 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..4 order.
1
1, 2, 5, 13, 44, 167, 695, 3070, 14074, 65958, 313098, 1497216, 7189646, 34606966, 166803484, 804596882, 3882748894, 18741593296, 90476092366, 436812623774, 2108996095916, 10182801139146, 49166003981046, 237391983175872
OFFSET
1,2
COMMENTS
Column 4 of A212829.
LINKS
FORMULA
Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 20*a(n-3) + 10*a(n-4) + 24*a(n-5) + 8*a(n-6) for n>9.
Empirical g.f.: x*(1 + x + x^2)*(1 - 6*x + 3*x^2 + 15*x^3 - 9*x^5 - 3*x^6) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x - 4*x^2)). - Colin Barker, Jul 21 2018
EXAMPLE
Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....0....1....1....0....1....1....1....1....1....1
..2....2....2....2....2....2....1....2....2....1....2....2....0....0....1....1
..3....1....3....1....2....0....2....3....2....0....1....3....2....2....0....2
..4....0....0....1....0....3....2....1....0....2....1....2....0....0....1....2
..3....2....0....2....2....4....1....1....0....0....1....1....0....3....2....1
..0....2....2....2....2....2....0....0....1....3....3....1....2....1....3....2
..4....2....0....2....0....1....1....2....3....4....3....2....3....0....4....3
CROSSREFS
Cf. A212829.
Sequence in context: A119533 A375730 A066740 * A212826 A212827 A212828
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 28 2012
STATUS
approved