

A196294


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


1



3, 9, 20, 61, 187, 536, 1597, 4849, 14582, 44097, 134349, 409428, 1249517, 3822519, 11705002, 35866253, 109991817, 337493970, 1035913925, 3180693901, 9768462112, 30005758115, 92181317503, 283222651372, 870256732085, 2674196289015
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OFFSET

1,1


COMMENTS

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


LINKS



FORMULA

Empirical: a(n) = 2*a(n1) +4*a(n2) +6*a(n3) 9*a(n4) 38*a(n5) 32*a(n6) 11*a(n7) +6*a(n8) +a(n9).
Empirical g.f.: x*(1 + x)^2*(3  3*x  7*x^2  16*x^3  3*x^4 + 15*x^5 + 2*x^6) / ((1  x  7*x^3  x^4)*(1  x  5*x^2  4*x^3  x^4 + x^5)).  Colin Barker, May 08 2018


EXAMPLE

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



