A196488 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,0,1,4 for x=0,1,2,3,4.

1, 3, 9, 23, 69, 199, 553, 1563, 4439, 12591, 35645, 100885, 285753, 809481, 2292615, 6492777, 18388691, 52081399, 147506079, 417765845, 1183196095, 3351057703, 9490892585, 26880156625, 76130113051, 215616141961, 610669320471

Offset

1,2

Comments

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

Column 3 of A196493.

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-2) +6*a(n-3) +10*a(n-4) +15*a(n-5) +9*a(n-6) +4*a(n-7) +a(n-8).

Empirical g.f.: x*(1 + 2*x + 5*x^2 + 5*x^3 + 9*x^4 + 8*x^5 + 3*x^6 + x^7) / (1 - x - x^2 - 6*x^3 - 10*x^4 - 15*x^5 - 9*x^6 - 4*x^7 - x^8). - Colin Barker, May 09 2018

Example

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

Crossrefs

Cf. A196493.

Sequence in context: A164949 A146661 A004666 * A108488 A018334 A146392

Adjacent sequences: A196485 A196486 A196487 * A196489 A196490 A196491

Keyword

nonn

Author

R. H. Hardin, Oct 03 2011

Status

approved