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A196899 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,1,0,2 for x=0,1,2,3,4. 1
1, 3, 20, 71, 286, 1176, 4768, 19265, 78414, 318016, 1290577, 5238372, 21260925, 86285262, 350204527, 1421330461, 5768590644, 23412347684, 95021149248, 385651641498, 1565201886761, 6352511449133, 25782234607765, 104639500545470 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Column 3 of A196904.

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) +7*a(n-2) +8*a(n-3) -2*a(n-4) -33*a(n-5) +2*a(n-6) -6*a(n-7) -14*a(n-8) +a(n-9) +2*a(n-10).

Empirical g.f.: x*(1 + x + 7*x^2 + 2*x^3 - 18*x^4 - 14*x^5 - 17*x^6 + 11*x^7 + 7*x^8 - 2*x^9) / (1 - 2*x - 7*x^2 - 8*x^3 + 2*x^4 + 33*x^5 - 2*x^6 + 6*x^7 + 14*x^8 - x^9 - 2*x^10). - Colin Barker, May 09 2018

EXAMPLE

Some solutions for n=4:

..0..3..0....0..3..0....0..3..0....0..0..0....0..0..0....0..3..0....0..1..0

..3..0..0....0..0..3....3..0..3....0..0..0....1..3..0....3..0..3....0..3..0

..0..0..3....3..0..0....0..0..0....3..0..0....0..0..3....0..3..0....3..0..3

..0..3..0....0..3..0....0..0..0....0..0..0....0..0..0....0..1..0....0..3..0

CROSSREFS

Cf. A196904.

Sequence in context: A160456 A289643 A196741 * A006411 A243208 A129549

Adjacent sequences:  A196896 A196897 A196898 * A196900 A196901 A196902

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 07 2011

STATUS

approved

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Last modified January 20 22:57 EST 2020. Contains 331104 sequences. (Running on oeis4.)