A197524 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,4,1,0,1 for x=0,1,2,3,4.

1, 3, 32, 69, 308, 1444, 5048, 20265, 83277, 322864, 1280598, 5112008, 20189827, 80032884, 317712722, 1258773307, 4990157041, 19788837323, 78445935632, 310998937948, 1233039388705, 4888402255720, 19380385472489, 76835860723308

Offset

1,2

Comments

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

Column 3 of A197529.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +2*a(n-2) +19*a(n-3) +10*a(n-4) +21*a(n-5) +31*a(n-6) -99*a(n-7) -9*a(n-8) +16*a(n-9).

Empirical g.f.: x*(1 + x + 24*x^2 - 20*x^3 + 39*x^4 + 31*x^5 - 181*x^6 + 73*x^7) / (1 - 2*x - 2*x^2 - 19*x^3 - 10*x^4 - 21*x^5 - 31*x^6 + 99*x^7 + 9*x^8 - 16*x^9). - Colin Barker, May 13 2018

Example

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

Crossrefs

Cf. A197529.

Sequence in context: A324223 A197368 A114257 * A107465 A319219 A345687

Adjacent sequences: A197521 A197522 A197523 * A197525 A197526 A197527

Keyword

nonn

Author

R. H. Hardin, Oct 16 2011

Status

approved