A221543 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.

3, 22, 103, 303, 716, 1455, 2658, 4487, 7128, 10791, 15710, 22143, 30372, 40703, 53466, 69015, 87728, 110007, 136278, 166991, 202620, 243663, 290642, 344103, 404616, 472775, 549198, 634527, 729428, 834591, 950730, 1078583, 1218912

Offset

1,1

Comments

Row 5 of A221542.

Links

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

Formula

Empirical: a(n) = 1*n^4 + 1*n^3 - 3*n^2 + 10*n - 9 for n>3.

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

G.f.: x*(3 + 7*x + 23*x^2 - 22*x^3 + 26*x^4 - 18*x^5 + 6*x^6 - x^7) / (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
..0....4....5....4....0....2....3....0....5....0....0....2....0....3....0....6
..1....0....5....5....1....6....4....0....0....2....0....2....3....4....2....6
..4....4....1....3....6....2....0....3....2....1....3....3....6....6....0....1
..6....6....6....1....3....4....0....0....5....3....6....1....3....6....5....6

Crossrefs

Cf. A221542.

Sequence in context: A254332 A009029 A009032 * A309000 A352027 A061182

Adjacent sequences: A221540 A221541 A221542 * A221544 A221545 A221546

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved