A197884 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4

1, 3, 6, 47, 77, 196, 529, 1637, 4235, 11211, 30271, 83254, 225148, 606579, 1638498, 4440639, 12016918, 32485381, 87846790, 237662631, 642926239, 1738933011, 4703362637, 12722244082, 34413103568, 93083202626, 251777401480

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 1's, every 4 is next to 4 1's.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = a(n-1) +a(n-2) +4*a(n-3) +12*a(n-4) +7*a(n-5) +21*a(n-6) -22*a(n-7) -6*a(n-8) -64*a(n-9) -136*a(n-10) +16*a(n-11) +112*a(n-12) +621*a(n-13) +473*a(n-14) +396*a(n-15) -294*a(n-16) -1044*a(n-17) -744*a(n-18) -475*a(n-19) +1462*a(n-20) +156*a(n-21) -1601*a(n-22) -627*a(n-23) -2504*a(n-24) -1566*a(n-25) +468*a(n-26) -518*a(n-27) +384*a(n-28) +444*a(n-29) +208*a(n-30) +400*a(n-31) +96*a(n-32).

Empirical formula verified: see link. - Robert Israel, Aug 24 2018

Example

Some solutions for n=4
..1..2..0....1..1..0....1..1..2....0..1..1....2..1..0....0..1..2....0..1..2
..0..1..1....2..2..1....2..3..1....1..2..2....1..1..2....1..0..1....1..4..1
..1..1..2....1..0..1....1..1..3....1..3..1....1..4..1....2..2..1....2..1..1
..2..1..0....0..1..2....0..2..1....2..1..0....2..1..0....1..1..0....0..1..2

Crossrefs

Column 3 of A197889.

Sequence in context: A038050 A194080 A261841 * A279706 A032322 A203765

Adjacent sequences: A197881 A197882 A197883 * A197885 A197886 A197887

Keyword

nonn

Author

R. H. Hardin, Oct 19 2011

Status

approved