A221544 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by something other than 1, starting with 0.

5, 54, 364, 1386, 4018, 9665, 20386, 39007, 69242, 115813, 184570, 282611, 418402, 601897, 844658, 1159975, 1562986, 2070797, 2702602, 3479803, 4426130, 5567761, 6933442, 8554607, 10465498, 12703285, 15308186, 18323587, 21796162, 25775993

Offset

1,1

Comments

Row 6 of A221542.

Links

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

Formula

Empirical: a(n) = 1*n^5 + 2*n^4 - 6*n^3 + 21*n^2 - 31*n + 23 for n>4.

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

G.f.: x*(5 + 24*x + 115*x^2 - 88*x^3 + 157*x^4 - 153*x^5 + 87*x^6 - 34*x^7 + 8*x^8 - x^9) / (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>10.

(End)

Example

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

Crossrefs

Cf. A221542.

Sequence in context: A275261 A208429 A275353 * A268882 A229298 A087125

Adjacent sequences: A221541 A221542 A221543 * A221545 A221546 A221547

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved