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A197058
Number of n X 5 0..4 arrays with each element equal to the number its horizontal and vertical neighbors equal to 2.
1
1, 5, 14, 28, 48, 90, 200, 447, 937, 1881, 3813, 7947, 16720, 34862, 71998, 148612, 308152, 640701, 1330955, 2759769, 5719391, 11860647, 24611330, 51069476, 105937956, 219719928, 455740768, 945408061, 1961252075, 4068435185
OFFSET
1,2
COMMENTS
Every 0 is next to 0 2's, every 1 is next to 1 2's, every 2 is next to 2 2's, every 3 is next to 3 2's, every 4 is next to 4 2's.
Column 5 of A197061.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) +2*a(n-4) +3*a(n-5) -a(n-6) -2*a(n-7) -2*a(n-8) +2*a(n-9) -2*a(n-10) -a(n-11) -3*a(n-12) -a(n-13).
Empirical g.f.: x*(1 + 3*x + 5*x^2 + 4*x^3 - x^4 - 5*x^5 - 2*x^6 - 2*x^7 - x^8 - 6*x^9 - 5*x^10 - 4*x^11 - x^12) / (1 - 2*x + x^2 - x^3 - 2*x^4 - 3*x^5 + x^6 + 2*x^7 + 2*x^8 - 2*x^9 + 2*x^10 + x^11 + 3*x^12 + x^13). - Colin Barker, May 11 2018
EXAMPLE
Some solutions for n=4:
..0..0..0..1..1....1..2..2..2..2....2..2..2..1..0....0..1..1..1..1
..0..0..1..2..2....1..2..3..3..2....2..4..2..1..0....1..2..2..2..2
..0..0..1..2..2....1..2..2..2..2....2..2..2..1..0....1..2..3..3..2
..0..0..0..1..1....0..1..1..1..1....1..1..1..0..0....1..2..2..2..2
CROSSREFS
Cf. A197061.
Sequence in context: A134238 A024800 A005586 * A212678 A244100 A031333
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 09 2011
STATUS
approved