

A199142


Number of n X 1 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.


3



0, 1, 1, 2, 3, 6, 11, 23, 47, 102, 221, 492, 1099, 2485, 5637, 12858, 29391, 67354, 154539, 355003, 816035, 1876862, 4318201, 9937840, 22874731, 52659593, 121237417, 279141170, 642732027, 1479959118, 3407837387, 7847200511
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OFFSET

1,4


COMMENTS



LINKS



FORMULA

Empirical: a(n) = 3*a(n1) + a(n2)  7*a(n3) + a(n4) + 3*a(n5) for n>6.
Empirical g.f.: x^2*(1  2*x  2*x^2 + 3*x^3 + x^4) / ((1  x)*(1  x  x^2)*(1  x  3*x^2)).  Colin Barker, Feb 22 2018


EXAMPLE

Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....0....1....1....1....0....1....1....0....1....0....0....0....1....0
..1....1....0....1....1....1....1....1....1....0....1....0....0....0....1....0
..2....1....1....1....1....0....1....2....1....0....2....1....0....1....1....0
..2....1....1....0....2....0....0....2....1....1....2....1....0....1....1....0
..2....0....0....0....2....1....0....1....0....1....3....1....0....2....2....1
..2....0....0....0....2....1....0....1....0....1....3....1....0....2....2....1


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



