A196205 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,4,1 for x=0,1,2,3,4.

4, 8, 7, 14, 17, 27, 42, 58, 94, 137, 208, 319, 477, 732, 1108, 1686, 2573, 3912, 5975, 9113, 13914, 21268, 32504, 49733, 76116, 116561, 178607, 273786, 419924, 644346, 989153, 1519164, 2334105, 3587703, 5516702, 8486022, 13058268, 20100879

Offset

1,1

Comments

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

Column 3 of A196210.

Links

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

Formula

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

Empirical g.f.: x*(4 - 4*x - 9*x^2 + 9*x^3 - 3*x^4 + 8*x^5 - 7*x^6 + x^7 + 2*x^8) / ((1 - x)*(1 - x - x^3)*(1 - x - x^2 + x^4 - x^5)). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A196210.

Sequence in context: A201937 A211456 A309665 * A196141 A082210 A196282

Adjacent sequences: A196202 A196203 A196204 * A196206 A196207 A196208

Keyword

nonn

Author

R. H. Hardin, Sep 29 2011

Status

approved