

A196132


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


1



0, 4, 3, 8, 14, 19, 46, 56, 133, 184, 372, 599, 1064, 1874, 3147, 5692, 9516, 17053, 28980, 51004, 88089, 153086, 266660, 461205, 804810, 1392380, 2426083, 4205680, 7313450, 12699273, 22056242, 38328650, 66544359, 115648570, 200804584
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OFFSET

1,2


COMMENTS

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's.
Column 2 of A196138.


LINKS

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


FORMULA

Empirical: a(n) = 3*a(n2) +2*a(n3) 2*a(n4) 3*a(n5) a(n6) +4*a(n7) 2*a(n9).
Empirical g.f.: x^2*(4 + 3*x  4*x^2  3*x^3  3*x^4 + 6*x^5  4*x^7) / ((1  x)*(1 + x  2*x^2  4*x^3  2*x^4 + x^5 + 2*x^6  2*x^7  2*x^8)).  Colin Barker, May 08 2018


EXAMPLE

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


CROSSREFS

Cf. A196138.
Sequence in context: A309517 A105185 A165739 * A198179 A137503 A320263
Adjacent sequences: A196129 A196130 A196131 * A196133 A196134 A196135


KEYWORD

nonn


AUTHOR

R. H. Hardin, Sep 28 2011


STATUS

approved



