A211852 Number of nonnegative integer arrays of length 2n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

588, 2013, 5486, 12713, 26163, 49210, 86275, 142968, 226230, 344475, 507732, 727787, 1018325, 1395072, 1875937, 2481154, 3233424, 4158057, 5283114, 6639549, 8261351, 10185686, 12453039, 15107356, 18196186, 21770823, 25886448, 30602271

Offset

1,1

Comments

Row 6 of A211849.

Links

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

Formula

Empirical: a(n) = (71/60)*n^5 + (337/24)*n^4 + 67*n^3 + (3947/24)*n^2 + (12919/60)*n + 126.

Conjectures from Colin Barker, Jul 20 2018: (Start)

G.f.: x*(588 - 1515*x + 2228*x^2 - 1768*x^3 + 735*x^4 - 126*x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....1....1....1....1....1....0....1....1....1....1....1
..0....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
..0....2....2....1....2....0....2....2....2....2....1....2....1....1....2....0
..2....1....1....2....2....0....2....2....2....1....1....2....2....2....2....2
..2....1....1....2....2....2....1....2....3....1....0....3....2....2....2....2
..2....3....0....2....2....2....1....2....2....3....0....3....3....1....2....3
..3....3....0....3....3....3....3....3....3....1....2....3....3....1....2....3
..3....4....3....3....3....2....3....3....3....1....2....3....4....3....3....4
..4....4....3....4....4....2....3....2....4....2....3....3....3....1....3....4
..3....3....3....4....3....2....4....2....4....2....3....3....3....1....2....3
..3....4....4....4....3....4....4....2....5....4....4....4....1....4....2....3
..2....3....4....4....0....4....3....4....5....4....4....3....3....4....4....3

Crossrefs

Cf. A211849.

Sequence in context: A252387 A186395 A230716 * A178973 A259248 A238519

Adjacent sequences: A211849 A211850 A211851 * A211853 A211854 A211855

Keyword

nonn

Author

R. H. Hardin, Apr 22 2012

Status

approved