A198179 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

0, 4, 3, 8, 16, 21, 56, 70, 171, 256, 516, 905, 1622, 3048, 5293, 9992, 17564, 32517, 58330, 106144, 192767, 348188, 634426, 1145535, 2084360, 3771658, 6847617, 12413706, 22507930, 40835531, 74015802, 134288434, 243440863, 441575714

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 0's, every 4 is next to 4 0's.

Column 2 of A198185.

Links

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

Formula

Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -2*a(n-5) +4*a(n-7) -a(n-8) -3*a(n-9).

Empirical g.f.: x^2*(4 + 3*x - 4*x^2 - x^3 - x^4 + 6*x^5 - 3*x^6 - 7*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 2*x^4 - 4*x^7 - 3*x^8)). - Colin Barker, May 14 2018

Example

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

Crossrefs

Cf. A198185.

Sequence in context: A357587 A165739 A196132 * A137503 A320263 A215330

Adjacent sequences: A198176 A198177 A198178 * A198180 A198181 A198182

Keyword

nonn

Author

R. H. Hardin, Oct 21 2011

Status

approved