

A196917


Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,4,0 for x=0,1,2,3,4.


1



1, 3, 7, 12, 27, 58, 121, 257, 545, 1153, 2442, 5172, 10952, 23193, 49116, 104012, 220265, 466453, 987802, 2091857, 4429902, 9381153, 19866361, 42070767, 89092785, 188670778, 399545962, 846113942, 1791805877, 3794486938, 8035541856
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OFFSET

1,2


COMMENTS

Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 4's, every 4 is next to 4 0's.
Column 3 of A196922.


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200


FORMULA

Empirical: a(n) = 2*a(n1) +a(n3) a(n4) for n>5.
Empirical g.f.: x*(1 + x + x^2  3*x^3 + x^4) / (1  2*x  x^3 + x^4).  Colin Barker, May 09 2018


EXAMPLE

Some solutions for n=4:
..0..0..0....0..2..2....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..2..2..2....0..2..2....0..0..0....2..2..0....0..0..0....0..0..0....0..0..0
..2..0..2....0..0..0....0..2..2....2..2..0....2..2..0....0..4..0....0..0..0
..2..2..2....0..0..0....0..2..2....0..0..0....2..2..0....0..0..0....0..0..0


CROSSREFS

Cf. A196922.
Sequence in context: A301982 A196858 A099811 * A256259 A182941 A063072
Adjacent sequences: A196914 A196915 A196916 * A196918 A196919 A196920


KEYWORD

nonn


AUTHOR

R. H. Hardin, Oct 07 2011


STATUS

approved



