A209368 Number of n X 2 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z.

8, 39, 84, 129, 178, 338, 722, 1568, 3362, 7200, 15488, 33282, 71442, 153458, 329672, 708050, 1520768, 3266568, 7016258, 15070050, 32369058, 69525632, 149333762, 320753792, 688947200, 1479788802, 3178436450, 6826961250, 14663623752

Offset

1,1

Comments

Column 2 of A209374.

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 3*a(n-3) + a(n-4) - a(n-5) - a(n-6) for n>11.

Empirical g.f.: x*(8 + 31*x + 37*x^2 - 18*x^3 - 160*x^4 - 252*x^5 - 218*x^6 - 32*x^7 + 93*x^8 + 73*x^9 + 16*x^10) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Jul 09 2018

Example

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

Crossrefs

Cf. A209374.

Sequence in context: A329172 A346326 A003353 * A190097 A245135 A200157

Adjacent sequences: A209365 A209366 A209367 * A209369 A209370 A209371

Keyword

nonn

Author

R. H. Hardin, Mar 07 2012

Status

approved