A196013 Number of n X 4 0..4 arrays with each element equal to the number its horizontal and vertical neighbors within one of itself.

1, 1, 7, 25, 27, 91, 231, 455, 1135, 2693, 6041, 14257, 33349, 76941, 179553, 418345, 971503, 2261807, 5264419, 12243481, 28490729, 66295633, 154236017, 358872825, 835013523, 1942797397, 4520363539, 10517663443, 24471508585, 56938341019

Offset

1,3

Comments

Column 4 of A196017.

Links

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

Formula

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

Empirical g.f.: x*(1 + 4*x^2 + 12*x^3 - 15*x^4 - 9*x^5 - x^6 - 8*x^7 + x^8 - 3*x^9 + 2*x^10+ 6*x^11 + 2*x^12 - 2*x^13) / (1 - x - 2*x^2 - 4*x^3 + x^4 + 4*x^5 + 2*x^6 + 3*x^7 + 3*x^8 - x^10). - Colin Barker, May 08 2018

Example

Some solutions for n=5:
..2..3..3..2....2..2..3..2....2..3..2..2....2..2..2..0....2..2..3..2
..3..4..4..3....2..0..3..3....2..3..0..2....2..0..3..2....2..0..3..3
..3..4..3..3....3..3..3..3....0..3..2..3....3..3..4..3....3..3..3..3
..3..3..0..2....2..3..0..2....2..3..0..2....3..4..4..3....3..3..0..2
..2..3..2..2....0..2..2..2....2..3..2..2....2..3..3..2....2..3..2..2

Crossrefs

Cf. A196017.

Sequence in context: A246792 A178370 A034125 * A272366 A327107 A075926

Adjacent sequences: A196010 A196011 A196012 * A196014 A196015 A196016

Keyword

nonn

Author

R. H. Hardin, Sep 26 2011

Status

approved