A221575 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1.

6, 57, 342, 1293, 3734, 8991, 19014, 36497, 64998, 109059, 174326, 267669, 397302, 572903, 805734, 1108761, 1496774, 1986507, 2596758, 3348509, 4265046, 5372079, 6697862, 8273313, 10132134, 12310931, 14849334, 17790117, 21179318, 25066359

Offset

1,1

Comments

Row 5 of A221573.

Links

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

Formula

Empirical: a(n) = 1*n^5 + 1*n^4 - 2*n^3 + 12*n^2 - 15*n + 9 for n>2.

Conjectures from Colin Barker, Aug 08 2018: (Start)

G.f.: x*(6 + 21*x + 90*x^2 - 24*x^3 + 56*x^4 - 39*x^5 + 12*x^6 - 2*x^7) / (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>8.

(End)

Example

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

Crossrefs

Cf. A221573.

Sequence in context: A181430 A281557 A227813 * A001593 A261740 A296027

Adjacent sequences: A221572 A221573 A221574 * A221576 A221577 A221578

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved