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

1,1

Comments

Column 3 of A209374.

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

Example

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

Crossrefs

Sequence in context: A142934 A036564 A062639 * A288749 A358932 A039609

Adjacent sequences: A209366 A209367 A209368 * A209370 A209371 A209372

Keyword

nonn

Author

R. H. Hardin, Mar 07 2012

Status

approved