A221466 Number of 0..n arrays of length 7 with each element unequal to at least one neighbor, starting with 0.

8, 240, 1944, 8960, 30000, 81648, 192080, 405504, 787320, 1430000, 2459688, 4043520, 6397664, 9796080, 14580000, 21168128, 30067560, 41885424, 57341240, 77280000, 102685968, 134697200, 174620784, 223948800, 284375000, 357812208

Offset

1,1

Comments

Row 7 of A221463.

Links

R. H. Hardin, Table of n, a(n) for n = 1..135

Formula

Empirical: a(n) = 1*n^6 + 4*n^5 + 3*n^4.

Conjectures from Colin Barker, Aug 05 2018: (Start)

G.f.: 8*x*(1 + 23*x + 54*x^2 + 14*x^3 - 2*x^4) / (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=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..6....4....5....2....5....2....4....4....4....4....1....3....4....6....2....3
..6....4....0....2....4....0....4....3....3....4....2....4....5....4....1....2
..0....5....6....4....0....4....2....6....3....5....2....6....2....6....6....1
..0....3....1....2....1....4....0....4....6....2....0....1....3....5....4....1
..6....6....1....3....0....3....2....4....6....0....2....0....6....4....4....0
..2....2....6....0....6....1....1....3....3....3....5....3....5....6....5....4

Crossrefs

Cf. A221463.

Sequence in context: A240431 A222688 A254927 * A334712 A067360 A221770

Adjacent sequences: A221463 A221464 A221465 * A221467 A221468 A221469

Keyword

nonn

Author

R. H. Hardin, Jan 17 2013

Status

approved