A211837 Number of nonnegative integer arrays of length n+4 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value n+1.

33, 77, 157, 289, 492, 788, 1202, 1762, 2499, 3447, 4643, 6127, 7942, 10134, 12752, 15848, 19477, 23697, 28569, 34157, 40528, 47752, 55902, 65054, 75287, 86683, 99327, 113307, 128714, 145642, 164188, 184452, 206537, 230549, 256597, 284793, 315252

Offset

1,1

Comments

Row 3 of A211836.

Links

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

Formula

Empirical: a(n) = (1/8)*n^4 + (17/12)*n^3 + (51/8)*n^2 + (157/12)*n + 12.

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

G.f.: x*(33 - 88*x + 102*x^2 - 56*x^3 + 12*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
..1....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1
..1....2....2....2....1....2....2....2....0....2....2....1....2....2....0....0
..2....0....3....3....2....3....0....3....2....1....1....2....3....2....2....1
..3....3....4....1....3....4....3....0....3....3....3....3....4....3....3....2
..4....2....2....1....2....3....4....0....4....4....3....2....3....3....4....3
..2....4....2....4....4....5....1....4....3....3....4....4....4....4....5....4

Crossrefs

Cf. A211836.

Sequence in context: A248979 A246409 A378481 * A138863 A138866 A001987

Adjacent sequences: A211834 A211835 A211836 * A211838 A211839 A211840

Keyword

nonn

Author

R. H. Hardin, Apr 21 2012

Status

approved