A196141 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

4, 8, 7, 26, 49, 85, 178, 348, 683, 1349, 2688, 5319, 10498, 20818, 41206, 81574, 161646, 320215, 634294, 1256481, 2489029, 4930656, 9767642, 19350237, 38333645, 75940498, 150441579, 298031468, 590414638, 1169642000, 2317123308, 4590345948

Offset

1,1

Comments

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

Column 3 of A196146.

Links

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

Robert Israel, Maple-assisted proof of empirical recurrence

Formula

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

Empirical g.f.: x*(4 - 4*x - 9*x^2 + 17*x^3 - 11*x^4 - 5*x^5 - 4*x^6 + 14*x^8 + 4*x^9 + 12*x^10) / (1 - 3*x + 2*x^2 - x^3 + 3*x^4 - 3*x^5 + x^6 + 7*x^8 - x^9 - 4*x^10 - 2*x^11 - 6*x^12). - Colin Barker, May 08 2018

Empirical formulas verified: see link. - Robert Israel, Jan 21 2019

Example

Some solutions for n=4:
.0.1.1...1.1.0...0.0.0...1.0.0...1.0.1...0.0.1...0.0.1
.1.1.0...0.1.1...1.1.1...3.1.1...1.0.1...0.0.1...1.1.1
.3.1.1...1.1.3...1.1.3...1.1.1...1.0.1...0.0.1...1.1.0
.1.0.1...1.0.1...0.0.1...0.0.0...1.0.1...0.0.1...0.1.1

Crossrefs

Cf. A196146.

Sequence in context: A211456 A309665 A196205 * A082210 A196282 A196332

Adjacent sequences: A196138 A196139 A196140 * A196142 A196143 A196144

Keyword

nonn

Author

R. H. Hardin, Sep 28 2011

Status

approved