A221598 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less.

64, 393, 1210, 2715, 5082, 8475, 13056, 18987, 26430, 35547, 46500, 59451, 74562, 91995, 111912, 134475, 159846, 188187, 219660, 254427, 292650, 334491, 380112, 429675, 483342, 541275, 603636, 670587, 742290, 818907, 900600, 987531, 1079862

Offset

1,1

Comments

Row 6 of A221596.

Links

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

Formula

Empirical: a(n) = 27*n^3 + 108*n^2 - 252*n + 267 for n>3.

Conjectures from Colin Barker, Aug 09 2018: (Start)

G.f.: x*(64 + 137*x + 22*x^2 - 23*x^3 - 26*x^4 - 10*x^5 - 2*x^6) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.

(End)

Example

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

Crossrefs

Cf. A221596.

Sequence in context: A228759 A220976 A249984 * A017618 A343724 A231841

Adjacent sequences: A221595 A221596 A221597 * A221599 A221600 A221601

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved