A221465 Number of 0..n arrays of length 6 with each element unequal to at least one neighbor, starting with 0.

5, 88, 513, 1856, 5125, 11880, 24353, 45568, 79461, 131000, 206305, 312768, 459173, 655816, 914625, 1249280, 1675333, 2210328, 2873921, 3688000, 4676805, 5867048, 7288033, 8971776, 10953125, 13269880, 15962913, 19076288, 22657381, 26757000

Offset

1,1

Comments

Row 6 of A221463.

Links

R. H. Hardin, Table of n, a(n) for n = 1..136

Formula

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

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

G.f.: x*(5 + 58*x + 60*x^2 - 2*x^3 - x^4) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A221463.

Sequence in context: A208019 A297529 A300135 * A184239 A054954 A266064

Adjacent sequences: A221462 A221463 A221464 * A221466 A221467 A221468

Keyword

nonn

Author

R. H. Hardin, Jan 17 2013

Status

approved