A221457 Number of 0..6 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..6 order.

0, 1, 2, 7, 25, 102, 456, 2218, 11605, 64647, 379349, 2320555, 14658240, 94843284, 624544847, 4164947151, 28025750099, 189783308469, 1290899153376, 8808076870934, 60230644078721, 412493027114619, 2827998455493193

Offset

1,3

Comments

Column 6 of A221459.

Links

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

Formula

Empirical: a(n) = 16*a(n-1) - 79*a(n-2) + 70*a(n-3) + 361*a(n-4) - 372*a(n-5) - 964*a(n-6) + 144*a(n-7) + 1116*a(n-8) + 720*a(n-9) + 144*a(n-10).

Empirical g.f.: x^2*(1 - 14*x + 54*x^2 + x^3 - 246*x^4 - 41*x^5 + 411*x^6 + 364*x^7 + 91*x^8) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 4*x - 4*x^2)*(1 - 6*x - 6*x^2)). - Colin Barker, Aug 05 2018

Example

Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....2....2....2....2....2....1....2....1....2....2....0....2....0....2....2
..1....0....1....3....1....3....2....3....0....1....0....2....2....2....3....1
..3....3....2....1....2....0....2....2....0....0....2....0....0....3....2....2
..1....2....3....2....0....4....3....1....1....1....3....1....1....4....4....1

Crossrefs

Cf. A221459.

Sequence in context: A150511 A036784 A221456 * A221458 A221453 A097597

Adjacent sequences: A221454 A221455 A221456 * A221458 A221459 A221460

Keyword

nonn

Author

R. H. Hardin, Jan 17 2013

Status

approved