

A196858


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


1



1, 3, 7, 12, 26, 56, 113, 235, 490, 1012, 2099, 4356, 9026, 18714, 38806, 80450, 166797, 345830, 717003, 1486565, 3082117, 6390162, 13248759, 27468753, 56951126, 118077121, 244810064, 507566235, 1052340264, 2181823742, 4523588913
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OFFSET

1,2


COMMENTS

Every 0 is next to 0 3's, every 1 is next to 1 4's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 1's.
Column 3 of A196863.


LINKS

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


FORMULA

Empirical: a(n) = 2*a(n1) a(n2) +3*a(n3) 2*a(n4) +2*a(n5) a(n6).
Empirical g.f.: x*(1 + x + 2*x^2  2*x^3 + 2*x^4  x^5) / (1  2*x + x^2  3*x^3 + 2*x^4  2*x^5 + x^6).  Colin Barker, May 09 2018


EXAMPLE

Some solutions for n=4:
..0..0..0....2..2..0....0..0..0....0..2..2....0..0..0....0..0..0....0..0..0
..2..2..0....2..2..0....0..2..2....0..2..2....0..1..0....0..0..0....0..0..0
..2..2..0....0..0..0....0..2..2....0..0..0....1..4..1....0..0..0....0..2..2
..0..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..0..0....0..2..2


CROSSREFS

Cf. A196863.
Sequence in context: A280345 A062325 A301982 * A099811 A196917 A256259
Adjacent sequences: A196855 A196856 A196857 * A196859 A196860 A196861


KEYWORD

nonn


AUTHOR

R. H. Hardin, Oct 06 2011


STATUS

approved



