A221516 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more, starting with 0.

0, 3, 30, 130, 381, 884, 1765, 3174, 5285, 8296, 12429, 17930, 25069, 34140, 45461, 59374, 76245, 96464, 120445, 148626, 181469, 219460, 263109, 312950, 369541, 433464, 505325, 585754, 675405, 774956, 885109, 1006590, 1140149, 1286560

Offset

1,2

Comments

Row 5 of A221515.

Links

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

Formula

Empirical: a(n) = 1*n^4 - 1*n^3 - 10*n^2 + 33*n - 34 for n>3.

Conjectures from Colin Barker, Aug 06 2018: (Start)

G.f.: x^2*(3 + 15*x + 10*x^2 + x^3 - 6*x^4 + 2*x^5 - x^6) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.

(End)

Example

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

Crossrefs

Cf. A221515.

Sequence in context: A031205 A225018 A365290 * A174774 A020874 A161806

Adjacent sequences: A221513 A221514 A221515 * A221517 A221518 A221519

Keyword

nonn

Author

R. H. Hardin, Jan 18 2013

Status

approved