A211851 Number of nonnegative integer arrays of length 2n+6 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

196, 561, 1302, 2619, 4755, 7996, 12671, 19152, 27854, 39235, 53796, 72081, 94677, 122214, 155365, 194846, 241416, 295877, 359074, 431895, 515271, 610176, 717627, 838684, 974450, 1126071, 1294736, 1481677, 1688169, 1915530, 2165121, 2438346

Offset

1,1

Comments

Row 5 of A211849.

Links

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

Formula

Empirical: a(n) = (43/24)*n^4 + (185/12)*n^3 + (1217/24)*n^2 + (937/12)*n + 50.

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

G.f.: x*(196 - 419*x + 457*x^2 - 241*x^3 + 50*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Cf. A211849.

Sequence in context: A023108 A092231 A188247 * A089493 A088753 A063048

Adjacent sequences: A211848 A211849 A211850 * A211852 A211853 A211854

Keyword

nonn

Author

R. H. Hardin, Apr 22 2012

Status

approved