A195973 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4.

4, 14, 24, 36, 67, 134, 240, 432, 803, 1501, 2764, 5118, 9519, 17718, 32927, 61310, 114257, 213023, 397223, 741197, 1383497, 2583168, 4824204, 9012010, 16838364, 31466993, 58813148, 109939804, 205534006, 384287357, 718564103, 1343717638

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 1's, every 3 is next to 3 3's, every 4 is next to 4 4's.

Column 3 of A195978.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +a(n-3) +a(n-4) -6*a(n-5) -a(n-6) -4*a(n-7) +2*a(n-8) +2*a(n-9) +5*a(n-10) +2*a(n-11) -2*a(n-14) -a(n-15).

Empirical g.f.: x*(4 + 6*x - 4*x^2 - 16*x^3 - 23*x^4 - 14*x^5 + 23*x^7 + 26*x^8 + 19*x^9 + 9*x^10 - x^11 - 7*x^12 - 5*x^13 - x^14) / ((1 - x)*(1 + x^2)*(1 - x - x^2)*(1 - x^2 - 2*x^3 - 4*x^4 - 2*x^5 - x^6 + x^7 + x^8 + 2*x^9 + x^10)). - Colin Barker, May 08 2018

Example

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

Crossrefs

Cf. A195978.

Sequence in context: A043505 A277591 A017317 * A116963 A094930 A289665

Adjacent sequences: A195970 A195971 A195972 * A195974 A195975 A195976

Keyword

nonn

Author

R. H. Hardin, Sep 25 2011

Status

approved