A211838 Number of nonnegative integer arrays of length n+5 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value n+1.

146, 461, 1254, 2997, 6451, 12766, 23596, 41229, 68732, 110111, 170486, 256281, 375429, 537592, 754396, 1039681, 1409766, 1883729, 2483702, 3235181, 4167351, 5313426, 6711004, 8402437, 10435216, 12862371, 15742886, 19142129, 23132297

Offset

1,1

Comments

Row 4 of A211836.

Links

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

Formula

Empirical: a(n) = (1/48)*n^6 + (19/48)*n^5 + (51/16)*n^4 + (661/48)*n^3 + (835/24)*n^2 + (317/6)*n + 41.

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

G.f.: x*(146 - 561*x + 1093*x^2 - 1210*x^3 + 781*x^4 - 275*x^5 + 41*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....1....0....1....1....1....1....1....1....0....1....1....1....1
..2....1....2....2....1....2....2....1....0....2....1....1....0....2....2....2
..3....0....3....0....2....1....3....2....2....1....2....2....2....1....3....3
..4....2....0....3....0....0....4....3....3....2....2....3....3....0....2....4
..1....3....3....4....3....3....0....1....0....1....3....2....4....3....4....3
..0....3....0....4....4....4....5....4....1....3....4....3....4....4....1....5
..0....4....4....5....1....3....6....2....4....4....3....4....0....4....2....0

Crossrefs

Cf. A211836.

Sequence in context: A238579 A238028 A179572 * A158132 A043431 A183662

Adjacent sequences: A211835 A211836 A211837 * A211839 A211840 A211841

Keyword

nonn

Author

R. H. Hardin, Apr 21 2012

Status

approved