A209369 Number of n X 3 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z.

19, 84, 115, 242, 690, 1922, 5460, 15488, 43792, 124002, 351154, 994050, 2814300, 7968032, 22558752, 63867602, 180820962, 511936002, 1449380900, 4103455232, 11617609120, 32891508162, 93121689570, 263644006658, 746422898732

Offset: 1

Author

R. H. Hardin, Mar 07 2012

Keywords

• nonn

Comments

Column 3 of A209374.

Examples

			Some solutions for n=5:
..2..2..3....3..2..3....3..2..3....1..2..1....2..3..1....1..2..1....3..1..3
..1..3..1....1..2..1....1..2..1....3..1..3....2..1..3....3..1..3....1..3..2
..3..1..2....3..1..3....3..1..3....2..3..1....1..3..2....1..3..2....3..1..3
..1..3..1....1..3..1....1..3..1....2..1..3....3..1..3....3..1..2....2..2..1
..3..2..3....2..2..3....2..1..3....1..3..1....2..2..1....2..3..1....3..1..3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Empirical g.f.: x*(19 + 46*x - 53*x^2 - 83*x^3 - 252*x^4 - 315*x^5 - 423*x^6 - 476*x^7 - 163*x^8 + 111*x^9 + 122*x^10 + 35*x^11) / ((1 - 2*x - 2*x^2 - x^3)*(1 + 2*x^2 + 2*x^4 - x^6)). - Colin Barker, Feb 18 2018