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

Author

R. H. Hardin, Sep 26 2011

Keywords

• nonn

Comments

Column 4 of A196017.

Examples

			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
		

Links

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

Crossrefs

Cf. A196017.

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