A221678 - OEIS

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A221678

Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

0, 2, 5, 20, 68, 241, 844, 2966, 10413, 36568, 128408, 450913, 1583400, 5560186, 19524853, 68562444, 240760252, 845440977, 2968805844, 10425101678, 36608235997, 128551546480, 451414815600, 1585164405441, 5566379537040

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 3 of A221683.

LINKS

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

FORMULA

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

Empirical g.f.: x^2*(2 - x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - Colin Barker, Oct 19 2017

EXAMPLE

Some solutions for n=6

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

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

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

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

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

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

CROSSREFS

Sequence in context: A274239 A271858 A189734 * A297350 A027041 A355866

Adjacent sequences: A221675 A221676 A221677 * A221679 A221680 A221681

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 22 2013

STATUS

approved