A221574 Number of 0..n arrays of length 3 with each element differing from at least one neighbor by something other than 1.

2, 9, 26, 59, 114, 197, 314, 471, 674, 929, 1242, 1619, 2066, 2589, 3194, 3887, 4674, 5561, 6554, 7659, 8882, 10229, 11706, 13319, 15074, 16977, 19034, 21251, 23634, 26189, 28922, 31839, 34946, 38249, 41754, 45467, 49394, 53541, 57914, 62519, 67362

Offset: 1

Author

R. H. Hardin, Jan 20 2013

Keywords

• nonn

Comments

Row 3 of A221573.

Examples

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

Links

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

Crossrefs

Cf. A221573.

Formula

Empirical: a(n) = 1*n^3 - 1*n^2 + 3*n - 1.

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

G.f.: x*(2 + x)*(1 + x^2) / (1 - x)^4.

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

(End)