A197337 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,2,1,2 for x=0,1,2,3,4.

1, 5, 11, 38, 103, 297, 856, 2458, 7045, 20229, 58099, 166807, 478862, 1374798, 3947115, 11332271, 32534963, 93408015, 268175294, 769933854, 2210486645, 6346325657, 18220355429, 52310797713, 150184749648, 431181704516

Offset

1,2

Comments

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

Column 3 of A197342.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +4*a(n-3) +7*a(n-4) +4*a(n-5) +6*a(n-6) +2*a(n-7) -3*a(n-8) -4*a(n-9) -6*a(n-10) -4*a(n-11) +2*a(n-12).

Empirical g.f.: x*(1 + 3*x + x^2 + 12*x^3 + 8*x^5 + 7*x^6 - 8*x^7 - 5*x^8 - 7*x^9 - 6*x^10 + 3*x^11) / (1 - 2*x - 4*x^3 - 7*x^4 - 4*x^5 - 6*x^6 - 2*x^7 + 3*x^8 + 4*x^9 + 6*x^10 + 4*x^11 - 2*x^12). - Colin Barker, May 12 2018

Example

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

Crossrefs

Cf. A197342.

Sequence in context: A038708 A042719 A045717 * A302766 A369982 A212199

Adjacent sequences: A197334 A197335 A197336 * A197338 A197339 A197340

Keyword

nonn

Author

R. H. Hardin, Oct 13 2011

Status

approved