A211850 Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

63, 147, 286, 494, 785, 1173, 1672, 2296, 3059, 3975, 5058, 6322, 7781, 9449, 11340, 13468, 15847, 18491, 21414, 24630, 28153, 31997, 36176, 40704, 45595, 50863, 56522, 62586, 69069, 75985, 83348, 91172, 99471, 108259, 117550, 127358, 137697, 148581

Offset

1,1

Comments

Row 4 of A211849.

Links

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

Formula

Empirical: a(n) = (7/3)*n^3 + (27/2)*n^2 + (163/6)*n + 20.

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

G.f.: x*(63 - 105*x + 76*x^2 - 20*x^3) / (1 - x)^4.

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

(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....0....1....1....0....0....1....1....1....1....1....1....1....1....1
..1....1....0....1....1....1....1....1....1....1....1....1....1....1....0....0
..1....1....1....2....2....1....1....2....1....2....0....2....2....2....0....0
..2....2....1....2....2....0....2....2....2....2....0....2....2....2....0....0
..2....2....2....3....2....0....2....2....2....3....2....3....3....3....2....2
..2....3....2....3....3....2....3....3....3....2....0....3....3....3....2....2
..3....2....2....4....2....2....2....2....3....2....0....3....1....3....3....3
..2....2....3....4....2....3....2....2....4....4....3....0....1....4....3....3
..2....4....3....3....4....3....2....4....4....4....3....0....1....4....3....4
..4....4....4....3....2....4....4....4....2....0....4....4....4....5....4....4

Crossrefs

Cf. A211849.

Sequence in context: A031895 A044314 A044695 * A330433 A044395 A044776

Adjacent sequences: A211847 A211848 A211849 * A211851 A211852 A211853

Keyword

nonn

Author

R. H. Hardin, Apr 22 2012

Status

approved