A211853 Number of nonnegative integer arrays of length 2n+8 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

1731, 6936, 21897, 57913, 134164, 280751, 542235, 981675, 1685165, 2766870, 4374561, 6695649, 9963718, 14465557, 20548691, 28629411, 39201303, 52844276, 70234089, 92152377, 119497176, 153293947, 194707099, 245052011, 305807553

Offset

1,1

Comments

Row 7 of A211849.

Links

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

Formula

Empirical: a(n) = (499/720)*n^6 + (2587/240)*n^5 + (10031/144)*n^4 + (11681/48)*n^3 + (179153/360)*n^2 + (8788/15)*n + 323.

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

G.f.: x*(1731 - 5181*x + 9696*x^2 - 10295*x^3 + 6435*x^4 - 2210*x^5 + 323*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....1....1....1....1....0....1....1....1....0....1....1....0....1....1....1
..1....1....1....1....0....1....1....1....1....1....1....1....1....0....1....1
..2....2....1....2....1....0....1....2....2....1....2....2....1....0....2....1
..2....2....2....2....1....0....2....2....2....2....2....2....2....2....2....2
..3....2....2....2....2....2....2....3....3....1....0....3....2....0....3....2
..3....3....2....3....1....2....2....3....2....1....0....3....3....2....2....2
..2....3....3....3....2....3....2....4....2....3....0....1....3....2....3....3
..3....4....3....4....2....3....3....4....2....3....3....1....4....3....3....2
..3....3....3....4....2....4....2....5....4....3....3....4....3....3....4....2
..4....4....4....2....2....4....2....5....4....3....3....4....4....4....4....4
..3....3....4....2....3....2....4....6....0....4....4....1....4....3....0....4
..3....3....4....2....3....2....4....6....0....3....4....1....5....3....0....0
..4....4....0....3....4....3....5....2....5....4....0....0....4....0....0....4

Crossrefs

Cf. A211849.

Sequence in context: A258166 A130876 A234706 * A252454 A256807 A008745

Adjacent sequences: A211850 A211851 A211852 * A211854 A211855 A211856

Keyword

nonn

Author

R. H. Hardin, Apr 22 2012

Status

approved